Honors Chemistry Chapter 1 The Study of Change
Jan 03, 2016
Honors Chemistry
Chapter 1
The Study of Change
11 ndash 12 Chemistry
bull The study of matter and the changes it undergoes
bull Structure and properties of matter
bull Macroscopic vs Microscopic
bull Structure (microscopic) determines properties (macroscopic)
13 Scientific Method
bull Systematic approach to research
bull Based on data gathered by observationbull Qualitative ndash general observationsbull Quantitative ndash numeric data
bull Evolution of ideasbull Hypothesis ndash tentative explanation testablebull Theory ndash unifying principle that explains
observationsbull Scientific Law ndash mathematical relationship
14 Classification of Matter
bull Matter ndash anything with mass and volumebull Substance ndash matter with definite composition
and distinct propertiesbull Element ndash cannot be separated into simpler
substances (ie only one type of atom present)bull Examples aluminum gold sulfur oxygen neonbull Compound ndash two or more elements chemically
combined in fixed proportionsbull Examples water sulfuric acid rust baking soda
14 Classification of Matter
bull Mixture ndash combination of two or more substances which retain their identities
bull Homogeneous mixture ndash composition of mixture is uniform throughout
bull Examples saltwater air metal alloysbull Heterogeneous mixture ndash composition is
not uniform phase boundariesbull Examples salt and pepper oil and water
salad dressing
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
11 ndash 12 Chemistry
bull The study of matter and the changes it undergoes
bull Structure and properties of matter
bull Macroscopic vs Microscopic
bull Structure (microscopic) determines properties (macroscopic)
13 Scientific Method
bull Systematic approach to research
bull Based on data gathered by observationbull Qualitative ndash general observationsbull Quantitative ndash numeric data
bull Evolution of ideasbull Hypothesis ndash tentative explanation testablebull Theory ndash unifying principle that explains
observationsbull Scientific Law ndash mathematical relationship
14 Classification of Matter
bull Matter ndash anything with mass and volumebull Substance ndash matter with definite composition
and distinct propertiesbull Element ndash cannot be separated into simpler
substances (ie only one type of atom present)bull Examples aluminum gold sulfur oxygen neonbull Compound ndash two or more elements chemically
combined in fixed proportionsbull Examples water sulfuric acid rust baking soda
14 Classification of Matter
bull Mixture ndash combination of two or more substances which retain their identities
bull Homogeneous mixture ndash composition of mixture is uniform throughout
bull Examples saltwater air metal alloysbull Heterogeneous mixture ndash composition is
not uniform phase boundariesbull Examples salt and pepper oil and water
salad dressing
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
13 Scientific Method
bull Systematic approach to research
bull Based on data gathered by observationbull Qualitative ndash general observationsbull Quantitative ndash numeric data
bull Evolution of ideasbull Hypothesis ndash tentative explanation testablebull Theory ndash unifying principle that explains
observationsbull Scientific Law ndash mathematical relationship
14 Classification of Matter
bull Matter ndash anything with mass and volumebull Substance ndash matter with definite composition
and distinct propertiesbull Element ndash cannot be separated into simpler
substances (ie only one type of atom present)bull Examples aluminum gold sulfur oxygen neonbull Compound ndash two or more elements chemically
combined in fixed proportionsbull Examples water sulfuric acid rust baking soda
14 Classification of Matter
bull Mixture ndash combination of two or more substances which retain their identities
bull Homogeneous mixture ndash composition of mixture is uniform throughout
bull Examples saltwater air metal alloysbull Heterogeneous mixture ndash composition is
not uniform phase boundariesbull Examples salt and pepper oil and water
salad dressing
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
14 Classification of Matter
bull Matter ndash anything with mass and volumebull Substance ndash matter with definite composition
and distinct propertiesbull Element ndash cannot be separated into simpler
substances (ie only one type of atom present)bull Examples aluminum gold sulfur oxygen neonbull Compound ndash two or more elements chemically
combined in fixed proportionsbull Examples water sulfuric acid rust baking soda
14 Classification of Matter
bull Mixture ndash combination of two or more substances which retain their identities
bull Homogeneous mixture ndash composition of mixture is uniform throughout
bull Examples saltwater air metal alloysbull Heterogeneous mixture ndash composition is
not uniform phase boundariesbull Examples salt and pepper oil and water
salad dressing
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
14 Classification of Matter
bull Mixture ndash combination of two or more substances which retain their identities
bull Homogeneous mixture ndash composition of mixture is uniform throughout
bull Examples saltwater air metal alloysbull Heterogeneous mixture ndash composition is
not uniform phase boundariesbull Examples salt and pepper oil and water
salad dressing
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
14 Classification of Matter
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
15 States of Matter
solid liquid gas
melting
freezing
vaporizing
condensing
sublimation
deposition
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
16 Properties of Matter
bull Physical propertybull can be observed without changing the identity of
the substance
bull Physical changebull remains the same substance
bull Extensive propertybull Depends only on the amount of matter present
bull Intensive propertybull Depends on the type of matter present
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
16 Properties of Matter
bull Chemical propertybull Property involving reactions with other substances
bull Chemical changebull New substance is produced
bull Classify the following propertiesbull Color mass flammability solubility density
bull Classify the following changesbull Rusting cutting melting burning dissolving
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 SI Units
bull Systegraveme Internationale drsquoUnites
bull International System of Units
Base quantity Name Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 SI Conversions
Factor Name Symbol
1024 yotta Y
1021 zetta Z
1018 exa E
1015 peta P
1012 tera T
109 giga G
106 mega M
103 kilo k
102 hecto h
101 deka da
Factor Name Symbol
10-1 deci d
10-2 centi c
10-3 milli m
10-6 micro micro
10-9 nano n
10-12 pico p
10-15 femto f
10-18 atto a
10-21 zepto z
10-24 yocto y
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 SI Conversions
unitdahk mcdMGT pn
1 decimal place3 decimal places 3 decimal places
Some Practice
173 cm = ______ m0173 0025 kg = ______ mg25 000
587 nm = __________ cm0000 058 7
Multiply number of decimal places by the dimensionality of the unit
0986 dm3 = ______ cm3986
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 Derived Units
bull Mathematical combinations of base unitsbull Area A=lw mm = m2
bull Volume V = lwh m m m = m3
bull dm3 = Liter cm3 = mL
bull Density = mV kgm3 gcm3 gmL
bull Mass vs Weightbull Mass = amount of matter = kgbull Weight = force of gravity = N
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 Temperature Scales
Boiling PointBoiling Point
Freezing PointFreezing Point
Absolute ZeroAbsolute Zero
Fahrenheit
Coldest tempin lab = 0oF
Human bodytemp = 100oF
32oF
212oF
-460oF
Celsius
0oC
100oC
-27315oC
Kelvin
27315 K
37315 K
0 K
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
17 Temperature Conversions
bull Celsius-Kelvin offset by 27315o
bull K = oC + 27315bull oC = K ndash 27315
bull Celsius-Fahrenheitbull Offset by 32oFbull Different sized degrees 9Fo = 5Co
bull oC = 59 (oF - 32)bull oF = 95 oC + 32bull Convert 986oF to oC and to K
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
18 Scientific Notation
bull m x 10n
bull 1 le m lt 10
bull Exponentiation multiply exponents
bull Multiplication Add exponents
bull Division Subtract exponents
bull AdditionSubtraction must have same exponent
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
18 Significant DigitsDigits which were actually measured as opposed to placeholder zeroes
Considerhow long is the blue rectangle
1 2 3 4 5 cm
Read 2 cm Estimate the next digit 24 cm plusmn 01 cm
Letrsquos use a better ruler
Now how long is the rectangle
243 cm plusmn 001 cm
measurementx
uncertainty in measurement
x
Implied plusmn1 on last digit of all measurements unless told otherwise
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
18 Significant Digits
bull Rules of thumb to deal with calculations involving significant digits
bull AdditionSubtractionbull Round to the decimal place of the least precise
value
bull MultiplicationDivisionbull Round to the number of digits of the least precise
value
bull Answers must be rounded properly
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
18 Relative Error
bull Compare uncertainty to measurementbull x
RE = ------ x
bull Often expressed as a percentbull With laboratory data x is found by comparing
experimental result to theoretical expectationsbull | xth ndash xexp |
RE = --------------- xth
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
18 Accuracy and Precision
bull Accuracybull how close a measurement is to the correct valuebull How close were you to the bullrsquos eye
bull Precisionbull how closely a set of values agree with each otherbull Were your shots clustered or scattered
bull Letrsquos measure the bp of water 3 timesbull Accurate but not precise 96oC 101oC 104oCbull Precise but not accurate 572oC 568oC 571oC
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
19 Dimensional Analysis
bull Technique for solving problems by treating units of measure as algebraic quantities
bull Set up conversion factors
bull 18 in = __________ ft
bull We know 1 ft = 12 in
bull 18 in 1 ft------- x -------- = 1 12 in
15 ft
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it
19 Dimensional Analysis
bull Convert the speed of light (300 x 108 ms) to miles hour
bull 300 x 108 m 1 km 1 mile 3600 s------------------ x ---------- x ---------- x -------- 1 s 1000 m 16 km 1 hr
bull = 68 x 108 mihr
bull 2 sig dig because of km ndash mile conversion
bull That wasnrsquot so bad was it