1. Units and Measurement

2. It All Starts with a Ruler!!!

3. Math and Units Math- the language of Physics
SI Units – International System
MKS
Meter m
Mass kg
Time s
National Bureau of Standards
Prefixes

4. SI Unit Prefixes - Part I
Name
Symbol
Factor
tera- T
1012
giga- G
109
mega- M
106
kilo- k
103
hecto- h
102
deka- da
101

5. SI Unit Prefixes- Part II
Name
Symbol
Factor
deci- d
10-1
centi- c
10-2
milli- m
10-3
micro- μ
10-6
nano- n
10-9
pico- p
10-12
femto- f
10-15

6. The Seven Base SI Units
Quantity
Unit
Symbol
Length
meter m
Mass
kilogram kg
Temperature
kelvin K
Time
second s
Amount of Substance
mole
mol
Luminous Intensity
candela cd
Electric Current
ampere a

7. Derived SI Units (examples)
Quantity
unit
Symbol
Volume
cubic meter m3
Density
kilograms per cubic meter
kg/m3
Speed
meter per second
m/s
Newton
kg m/ s2 N
Energy
Joule (kg m2/s2) J
Pressure
Pascal (kg/(ms2) Pa

8. SI Unit Prefixes for Length
Name
Symbol
Analogy
gigameter Gm
109
megameter Mm
106
kilometer km
103
decimeter dm
10-1
centimeter cm
10-2
millimeter mm
10-3
micrometer μm
10-6
nanometer nm
10-9
picometer pm
10-12

9. M x 10n Scientific Notation M is the coefficient 1<M<10
10 is the base
n is the exponent or power of 10

10. Other Examples:
5.45E or
5.45 x 10^6

11. Numbers less than 1 will have a negative exponent.
A millionth of a second is:
sec 1x10-6
1.0E ^-6

12. Factor-Label Method of Unit Conversion
Example: Convert 5km to m:
Multiply the original measurement by a conversion factor.
NEW UNIT
85km x 1,000m = ,000m
1km
OLD UNIT

13. Factor-Label Method of Unit Conversion: Example
Example: Convert 789m to km:
789m x 1km =0.789km= 7.89x10-1km
1000m

14. Convert 75.00 km/h to m/s 75.00 km x 1000 m x 1 h___ = 20.83m/s
h km s

15. Limits of Measurement
Accuracy and Precision

16. Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

17. Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

18. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

19. Example: Precision
Who is more precise when measuring the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

21. Example: Evaluate whether the following are precise, accurate or both.
Not Precise
Not Accurate
Precise
Accurate
Precise

22. Significant Figures
The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

23. Centimeters and Millimeters

24. Finding the Number of Sig Figs:
When the decimal is present, start counting from the left.
When the decimal is absent, start counting from the right.
Zeroes encountered before a non zero digit do not count.

25. How many sig figs?
0.001
x104

26. Sig Figs in Addition/Subtraction
Express the result with the same number of decimal places as the number in the operation with the least decimal places.
Ex: cm cm
5.3 cm
(Result is rounded to one decimal place)

27. Sig Figs in Multiplication/Division
Express the answer with the same sig figs as the factor with the least sig figs.
Ex: cm
x cm
6.4 cm2 (Result is rounded to two sig figs)

28. Counting Numbers
Counting numbers have infinite sig figs.
Ex: 3 apples

29. Solving Word Problems Analyze List knowns and unknowns.
Draw a diagram.
Devise a plan.
Write the math equation to be used.
Calculate
If needed, rearrange the equation to solve for the unknown.
Substitute the knowns with units in the equation and express the answer with units.
Evaluate
Is the answer reasonable?