Chapter 2 Measurement. Ch 2.1 - Measurement A. Measurement is a way to describe the world with numbers 1. Answers questions such as how much, how long,

Chapter 2Chapter 2MeasurementMeasurement

Ch 2.1Ch 2.1 - Measurement - Measurement

A.A. MeasurementMeasurement is a way to describe is a way to describe the world with numbersthe world with numbers

1. Answers questions such as how 1. Answers questions such as how much, how long, how far, etc.much, how long, how far, etc.

2. Can answer questions of volume, 2. Can answer questions of volume, mass weight, temperature and speedmass weight, temperature and speed

a) a) VolumeVolume – the amount of space an object – the amount of space an object occupiesoccupies

b) b) MassMass – how much matter is in an object – how much matter is in an object

c) c) WeightWeight – magnitude of gravitational – magnitude of gravitational force acting on an objectforce acting on an object

d) d) SpeedSpeed – relationship between a – relationship between a distance traveled and time taken to distance traveled and time taken to traveltravel

B.B. EstimationEstimation

1. Is a means of making a rough 1. Is a means of making a rough measurement of an objectmeasurement of an object

C. C. Precision & AccuracyPrecision & Accuracy

1. 1. PrecisionPrecision – a description of how – a description of how close measurements are to each close measurements are to each otherother

ex: ex: If you measure the same If you measure the same object 5 object 5 times and get the exact times and get the exact same result same result you have been precise you have been precise

2. 2. PrecisionPrecision (continued) (continued) - also how small of - also how small of a unit an object was measured toa unit an object was measured to

ex: ex: a ruler that shows mm is more a ruler that shows mm is more precise than one that only shows cmprecise than one that only shows cm

3. 3. AccuracyAccuracy – how close your measured – how close your measured value is to the accepted value value is to the accepted value (correctness)(correctness)

ex: ex: A clock with a second hand is A clock with a second hand is very very precise, however if it is set an precise, however if it is set an hour off, hour off, the time would not be the time would not be accurateaccurate

ex: ex: If you measure the length of a If you measure the length of a table to be 1.95m you have been more table to be 1.95m you have been more precise than if you just said 2m; precise than if you just said 2m; however if the table is 3m you were however if the table is 3m you were not very accuratenot very accurate

Precision vs. AccuracyPrecision vs. Accuracy

High Precision / Low Accuracy

High Accuracy / Low Precision

4. 4. Significant DigitsSignificant Digits - the # of digits that - the # of digits that reflect the precision of a measurementreflect the precision of a measurement

a) Digits other than 0 are always a) Digits other than 0 are always significantsignificant

b) Final 0’s after a decimal are b) Final 0’s after a decimal are significantsignificant

ex: ex: 6.54566.54560000 (shows this was (shows this was measured to the millionths place)measured to the millionths place)

c) 0’s between any other digits are significantc) 0’s between any other digits are significant

ex: ex: 55007.7.0033001 (present as place 1 (present as place holders)holders)

d) 0’s in a whole # may or may not be sig.d) 0’s in a whole # may or may not be sig.

ex: ex: 16516500 (depends on if it was a (depends on if it was a rounded # or not)rounded # or not)

e) A # obtained by counting instead of e) A # obtained by counting instead of measuring is significantmeasuring is significant

ex: ex: number of people in a roomnumber of people in a room

D. D. Rules for Significant FiguresRules for Significant Figures

1. 1. For x and ÷ For x and ÷ you must determine you must determine the amount of sig. digits in each # of the amount of sig. digits in each # of the problem. The # of sig. digits in the problem. The # of sig. digits in the answer will be the lesser number the answer will be the lesser number from the problem.from the problem.

ex: ex: 6.23 x 3.1 = 19.3136.23 x 3.1 = 19.313

3 2 2

2. 2. For + and – For + and – you must determine the you must determine the place value of each # in the problem. place value of each # in the problem. The sig. digits of the answer is The sig. digits of the answer is determined by the # that is least determined by the # that is least precise.precise.

ex: 6.23ex: 6.23

3.13.1

9.339.33

+Hundredths place

Tenths place

Tenths place

Ch 2.2Ch 2.2 – SI Units – SI Units

A. A. SISI - Stands for the - Stands for the International System of International System of UnitsUnits aka the aka the Metric SystemMetric System

1. Developed by French scientists in 1793 1. Developed by French scientists in 1793 commissioned under Louis XVIcommissioned under Louis XVI

2. Today has become the most widely used 2. Today has become the most widely used system of measurement in the world for system of measurement in the world for both commerce and scienceboth commerce and science

3. Has been adopted by all nations as 3. Has been adopted by all nations as their primary system of measure their primary system of measure except 3 except 3

Liberia

Burma

United States

4. Units are based on the number 104. Units are based on the number 10

5. Uses base units which may have an 5. Uses base units which may have an attached prefix to change the base attached prefix to change the base into a larger or smaller unitinto a larger or smaller unit

K H D * d c mKilo Hec

toDec

aBAS

EDec

i

Cent

iMilli

1101001000 0.1 0.01

0.001

More SI PrefixesMore SI Prefixes

B. B. SI UnitsSI Units

1. 1. LengthLength – meter (m) – meter (m)

2. 2. VolumeVolume – liter (l or m ) – liter (l or m )

3. 3. MassMass – gram (g) – gram (g)

4. 4. TemperatureTemperature – Kelvin (K) or Celsius ( – Kelvin (K) or Celsius ( C) C)

3

o

5. 5. TimeTime – second (s) – second (s)

6. 6. Rate/SpeedRate/Speed – meters/second (m/s) – meters/second (m/s)

7. 7. WeightWeight – Newton (N) – Newton (N)

8. 8. Electric CurrentElectric Current – Ampere (A) – Ampere (A)

9. 9. PressurePressure – Pascal (Pa) – Pascal (Pa)

C. C. SI Units vs. US Customary SystemSI Units vs. US Customary System

1. 1. 1 m = 3.28 ft (about 3’ 3”)1 m = 3.28 ft (about 3’ 3”)

2. 2. 1 km = 0.62 miles (1 mi = 1.6 km) 1 km = 0.62 miles (1 mi = 1.6 km)

3. 3. 1 1 00 C = 33.8 C = 33.8 00 F (1 F (1 00F = -17.2 F = -17.2 00C)C)

4. 4. 1 K = -457.6 1 K = -457.6 00F (1 F (1 00F = 255.7 K)F = 255.7 K)

Ch 2.3Ch 2.3 – Drawings, Tables & Graphs – Drawings, Tables & Graphs

A. A. Are used to represent data in an Are used to represent data in an organized mannerorganized manner

1. 1. TablesTables – display information in – display information in rows and columns so that it is easier rows and columns so that it is easier to read and understandto read and understand

Which is Easier to Interpret?Which is Easier to Interpret? In container A, the water temperature was In container A, the water temperature was

recorded to be 40 C and there was 56 guppy recorded to be 40 C and there was 56 guppy movements. In Container B, the water was movements. In Container B, the water was at 42 C and the number of guppy at 42 C and the number of guppy movements increased to 70. In container C, movements increased to 70. In container C, the water temperature was reduced to 36 C the water temperature was reduced to 36 C and the number of times the guppy moved and the number of times the guppy moved also dropped bringing the count to 46also dropped bringing the count to 46........OROR

2. 2. GraphGraph – used to collect, organize – used to collect, organize and summarize data in a visual wayand summarize data in a visual way

a) Generally the relationships a) Generally the relationships between data are seen more clearly between data are seen more clearly in a graph form in a graph form

b) There are 3 basic types of graphs:b) There are 3 basic types of graphs:

lineline, , barbar, , circlecircle

1) 1) Line GraphLine Graph – shows relationship – shows relationship between 2 variables; must be between 2 variables; must be numbersnumbers

2) 2) Bar GraphBar Graph – shows rectangular – shows rectangular blocks or bars of varying sizes to blocks or bars of varying sizes to show relationships among variablesshow relationships among variables

3) 3) Circle GraphCircle Graph - (aka Pie Graph) - (aka Pie Graph) shows the parts of a whole; each shows the parts of a whole; each section represents a fraction of the section represents a fraction of the totaltotal

- A circle graph has 360- A circle graph has 36000 You must You must determine what part of that 360 each determine what part of that 360 each section will be equal tosection will be equal to

(**See example p.58)(**See example p.58)