Units and Measurements in Physics

Contributed by:
Jonathan James
The highlights are:
1. Math and units
2. Scientific notation
3. Unit conversion
4. Accuracy
5. Precision
6. Significant figures
1. Units
Mr. Berman
International Space Station
2. It All Starts with a Ruler!!!
3. Math and Units
• Math- the language of Physics
• SI Units – International System
• 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 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 kg/m3
cubic meter
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. • 9 min video about powers of 10 in length.
• http://powersof10.com/film
10. Scientific Notation
M x 10n
• M is the coefficient 1• 10 is the base
• n is the exponent or power of 10
11. Other Examples:
• 5.45E+6 or
• 5.45 x 10^6
12. Numbers less than 1 will have a
negative exponent.
A millionth of a second is:
0.000001 sec 1x10-6
1.0E-6 1.0^-6
13. Factor-Label Method of Unit
• Example: Convert 5km to m:
• Multiply the original measurement by a
conversion factor.
85km x 1,000m = 85,000m
14. Factor-Label Method of Unit
Conversion: Example
• Example: Convert 789m to km:
789m x 1km =0.789km= 7.89x10-1km
15. Convert 75.00 km/h to m/s
75.00 km x 1000 m x 1 h___ = 20.83m/s
h 1 km 3600 s
16. Limits of Measurement
• Accuracy and Precision
17. • Accuracy - a measure of how
close a measurement is to the
true value of the quantity being
18. Example: Accuracy
• Who is more accurate when
measuring a book that has a true
length of 17.0cm?
17.0cm, 16.0cm, 18.0cm, 15.0cm
15.5cm, 15.0cm, 15.2cm, 15.3cm
19. • Precision – a measure of how
close a series of measurements
are to one another. A measure of
how exact a measurement is.
20. Example: Precision
Who is more precise when measuring
the same 17.0cm book?
17.0cm, 16.0cm, 18.0cm, 15.0cm
15.5cm, 15.0cm, 15.2cm, 15.3cm
22. Example: Evaluate whether the
following are precise, accurate or
Accurate Not Accurate Accurate
Not Precise Precise Precise
23. Significant Figures
• The significant figures in a
measurement include all of the
digits that are known, plus one
last digit that is estimated.
24. Centimeters and Millimeters
25. 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.
26. How many sig figs?
100 10302.00
10302 1.0302x104
27. 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: 2.33 cm
+ 3.0 cm
5.3 cm
(Result is rounded to one decimal place)
28. Sig Figs in Multiplication/Division
• Express the answer with the same sig
figs as the factor with the least sig
• Ex: 3.22 cm
x 2.0 cm
6.4 cm2
(Result is rounded to two sig figs)
29. Counting Numbers
• Counting numbers have infinite sig
• Ex: 3 apples
30. 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
– Substitute the knowns with units in the equation and
express the answer with units.
• Evaluate
– Is the answer reasonable?