1. 1.2 Measurement in Experiments

2. Learning Objectives List basic SI units and quantities they describe
Convert measurements to scientific notation
Distinguish between accuracy & precision
Use significant figures in measurements & calculations

3. Numbers as Measurements
In science, numbers represent measurements
Numbers involve three things
Magnitude how much?
Dimensions length, mass, time
Units of what?

4. The SI system The standard measurement system for science Base units
Basic units that are not a combination of some other units
Derived units
Are combinations of base units

5. Base Units Physical Quantity (Dimension) Unit Abbreviation Mass
Kilogram kg
Length
Meter m
Time
Second s
Electric current
Ampere A
Temperature
Kelvin K
Luminous intensity
Candela cd
Amount of substance
Mole
mol

6. Derived units Derived units are combinations of base units Base Unit
m (length)
m3 (volume)
kg (mass)
s (time)
N (newton) for force
1N = 1 kg∙m s2

7. Prefixes indicate orders of magnitude (powers of 10)
Abbrev
10 -18
atto- a
10 -1
deci- d
10 -15
femto- f
10 1
deka- da
10 -12
pico- p
10 3
kilo- k
10 -9
nano- n
10 6
mega- M
10 -6
micro- μ
10 9
giga- G
10 -3
milli- m
10 12
tera- T
10 -2
centi- c
10 15
peta- P

8. Converting Prefixes & Units
The main idea: multiply the given unit by a conversion factor yielding the desired unit
Conversion factor: a ratio of two units that is an equivalent to 1.
Example: convert millimeters to meters
1 mm x m = 1 x 10-3 m
1 mm
Practice 1A, #1-5

9. Converting units of area and units of volume
How many cm2 are in 1 m2?
How many cm3 are in 1 m3?
How many in3 are in 1 L?

10. Scientific Method A way of thinking and problem solving
A group of related processes and activities

11. Scientific Method: Important Terms
Law vs. Theory
Fact / Observation
Hypothesis
Experiment

12. Accuracy & Precision Accuracy Precision
Nearness of a measurement to the true value
Precision
Degree of exactness or refinement of a measurement
Repeatability of a measurement

13. Precision describes the limit of exactness of a measuring instrument
Significant figures reflect certainty of a measurement
Are figures that are known because they are measured

14. Significant Figures
Represent numbers known with certainty plus one final estimated digit
Reflect the precision of an instrument or measurement
Must be reported properly
Require special handling in calculations

15. Rules to determine significant digits
1. All non-zeros ARE
2. All zeros between non-zeros ARE
3. Zeros in front of non-zeros ARE NOT
4. Final zeros to right of decimal ARE
Final zeros without a decimal ARE NOT

16. How many significant figures?
x 103
x 10-4
x 107

17. Rules of calculating with significant figures
When adding & subtracting, final answer must have fewest decimal places present in the calculation.
When multiplying & dividing, final answer must have fewest significant digits present in the calculation.
Number of figures in a constant are ignored wrt sig figs.

18. 1.3 Language of Physics
Physical quantities often relate to one another in a mathematical way
Data is collected in a table form
Data is graphed
to show relationship of independent & dependent variables
When time is a variable it is usually the independent (x) variable
Manipulated & responding variables

19. Data Table and Graph Determining k through displacement x (m)
Force (N)
mass (kg)
0.00
0.01
0.49
0.05
0.03
0.98
0.10
0.06
1.47
0.15
0.09
1.96
0.20

20. Equations
Equations indicate relationships of variables

21. Evaluating Physics Equations: Dimensional Analysis
Can give you clues how to solve a problem
Can help check many types of problems because…
Dimensions can be treated as algebraic quantities
Example: derive a formula for speed
Example: How long would it take a car to travel 725 km at a speed of 88 km/h?

22. Order of Magnitude Estimates
Physics often uses very large and very small numbers
Using powers of ten as estimates of the numbers can help estimate and check your answers
Example: from the previous problem,