Matter And Measurement 1 Matter and Measurement. Matter And Measurement 2 Length The measure of how much space an object occupies; The basic unit of length,

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Matter and Measurement

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Length

• The measure of how much space an object occupies; The basic unit of length, or linear measure is the meters (m).

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Mass

• The basic unit of mass, or the amount of matter, is the kilograms (kg).

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Volume

• The most commonly used metric units for volume are the liter (L) and the milliliter (mL).□ A liter is a cube 1 dm long

on each side.□ A milliliter is a cube 1 cm

long on each side.

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Temperature:

A measure of the average kinetic energy of the particles in a sample.

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Temperature• In scientific

measurements, the Celsius and Kelvin scales are most often used.

• The Celsius scale is based on the properties of water.□ 0C is the freezing point

of water.□ 100C is the boiling point

of water.

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Temperature• The Kelvin is the SI

unit of temperature.• At 0 K, -273.15 C

(absolute zero) all molecule motion theoretically stops.

• There are no negative Kelvin temperatures.

• K = C + 273.15

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Temperature

• The Fahrenheit scale is not used in scientific measurements.

F = 9/5(C) + 32 C = 5/9(F − 32)

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SI Units

• Système International d’Unités• Uses different units and abbreviations for each

quantity

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Metric System

Prefixes help convert the base units into units that are appropriate for the item being measured.

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Metric System Conversions Factors

King

Henry

Died

By

drinking

chocolate

milk

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Dimensional Analysis

• Equality: An expression that says “this” equals “that”

1 hour 60 minutes

• Conversion factor : A ratio of the equivalent values in the equality

1 hour 60 minutes 60 minutes 1 hour

=

or

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Dimensional Analysis• Dimensional analysis : A method of problem-solving that helps

convert between the units used to describe matter

• This “t-chart” format is the same as:

# given units

# given units # find units

ratio of equality/conversion factor

# given units # find units# given units

x

problem

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Dimensional Analysis

Example 1: Oak Ridge students attend school from 7:16 am until 2:35 pm. This is 7.32 hours a day. How many minutes is this?

Given: 7.32 hours Equality: 1hour = 60 minutes

Find: # minutes Ratios: 1 hour 60 minutes 60 minutes 1 hour

7.32 hours

or

1 hour

60 minutes

= 7.32 x 60 minutes 1

= 439.2 minutes

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Dimensional Analysis/ Metric Conversions

1) A 5k (km) run is 3.1 miles. How many meters is this?

2) A 10k (km) run is 6.2miles. How many centimeters is this?

=

=

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More Conversion Problems

3) At 20 weeks a zygote is about 17cm. How many millimeters is this?

4) When eyes are dilated for an eye exam they expand 5 mm. How many cm is this?

=

=

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SCIENTIFIC NOTATION

• Because sometimes numbers are just too big or small to work with...........

M. x 10nbase number

exponent

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Scientific Notation

3.254 x 103

• Consists of a number with only ONE DIGIT to the LEFT of the decimal times some power of 10.

base number

exponent

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Standard Numeral to Scientific Notation:

1. Whole numbers will have:Positive power of 10, move decimal to left

Examples: 8,500 = 8 5 0 0. = 8.5 x 103

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Standard Numeral to Scientific Notation:

2. Decimal Numbers will have:negative power of 10; move decimal to right

Examples: 0.789 = 0 .7 8 9 = 7.89 x 10-

1

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Changing from Scientific Notation to Standard Numeral

1. If the exponent is (+): Move the decimal to the right!

Examples: 1.5 x 103 = 1.5 0 0 = 1500

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2. If the exponent is (-): Move the decimal to the left.

Examples: 2.63 x 10-3 = 0 0 2. 6 3 = .00263

Changing from Scientific Notation to Standard Numeral

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MATHEMATICAL CALCULATIONS USING SCIENTIFIC NOTATION

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MULTIPLICATION

A. Multiply base numbersB. Add powers of 10

Example: (1.5 x 103) ( 2.0 X 105) = 3.0 x 108

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DIVISION

A. Divide base numbersB. Subtract powers of 10 (numerator - denominator)

4.0 x 102 2.0 x 104

numerator

denominator

= 2.0 x 10-2

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ADDITION AND SUBTRACTION

*Exponents must be the SAME!

(6.5 x 102) + (2.0 x 103) + (30.0 x 103)

(0.65 x 103) + (2.0 x 103) + (30.0 x 103)

32.65 x 103 = 3.265 x 104

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Every answer should be written in correct scientific

notation!!

632 x 102 = 6.32 x 104

.0754 x 103 = 7.54 x 101

*Move decimal RIGHT = MORE NEGATIVE*Move decimal LEFT = MORE POSITIVE

*ALL NUMBERS IN THE BASE NUMBER ARE

SIGNIFICANT

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Uncertainty in Measurements• Different measuring devices have different uses

and different degrees of precision.

• The more subdivisions an instrument has, the more precise that instrument is.

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Which of the following is more precise? The one with more marks

between the same numbers.A B

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Reading InstrumentsStep 1 - Read the measurement to the smallest subdivision of

your instrument (Subdivision = the distance between two of the smallest lines)

Step 2 - Estimate one more digit

Example: What is the reading of the measurement below? _____

1 2

1.55

estimated digit

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Accuracy vs. Precision

•How close measurement comes to the true value of that measurement.

• How often you get the same measurement; reproducibility; consistent data.

• How close

measurements

are to each other

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Accuracy & Precision Examples

Neither accurate

nor precise

Precise but not

accurate

Precise AND

accurate

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Accuracy and Precision cont…

• Example: Three different groups of students (A, B, and C) measured the mass of the same piece of iron that has a known mass of 5.5 grams.

Which set is both precise and accurate? _______

A B CTrail 1 2.7 4.3 5.6Trial 2 2.7 5.8 5.5Trial 3 2.8 9.2 5.6

C

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Significant Figures

• The term significant figures refers to digits that were measured.

• When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

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Significant Figures

1. All non-zero digits are significant.

2. Zeroes in between two significant figures are themselves significant.

3. Zeroes at the beginning of a number are never significant.

4. Zeroes at the end of a number are significant if a decimal point is written in the number.

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Counting Significant Digits

43.00 m1.010 m9.000 m

1.000 x 103 m 0.01010 m

43,010 m

All of these measurements contain 4 significant digits.

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Calculating Using Sig Figs

1. Multiplying & Dividing1) Multiply or divide to get an answer

2) Round your answer to the LEAST number of SIGNIFICANT DIGITS

Example:

8.02 x 0.43 = 3.4486 = _______3.4

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Calculation practice

• 18.4cm2 / 2.30cm=

• 29.5 m x 3.1 m=

• 15.00 x.00003=

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Calculating Using Sig Figs2. Adding & Subtracting

1) Add or subtract to get an answer

2) Round your answer to the LEAST number of DECIMAL PLACES

Example: 4.3+ 5.4570 9.7570 = ________

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Calculation practice

29.00 99.8

+ 3.0041 - 12 0

0.0098

+ 2.32 0

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Which weighs more a ton of feathers or a ton of lead???

Density

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• The ratio that compares the mass of an object to its volume

• It is an intensive physical property;

• Units: g/mL or g/cm3

Density

Density = Mass 0Volume

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If substances do not mix, the less dense substance will float.

Density

1) What is the density of substance A? _______ 2) What is the density of substance D? _______ 3) If an object with a density of 0.95 g/mL is dropped into the column where would it settle? __________________

Given the densities of the four liquids:

0.69 g/mL 1.26 g/mL 1.00 g/mL 0.82 g/mL

0.69 g/mL

1.26 g/mL

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A block of wood measures 3.2 cm by 4.5 cm

by 6.1cm. When placed on the scale it

weighs 29 g. What is the density?

DensityExample 1

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A marble weighs 15grams. When placed in a graduated cylinder that had a volume of 29 mL of water in it, the water level raised to 34 mL. What is the density of the marble?

DensityExample 2

Final

Initial

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Pure Gold has a density of 19.32 g/cm3. If you have a chunk of gold that weighs 52 grams, what is the volume?

DensityExample 3