# Units and Measurements in Physics

Contributed by:
The highlights are:
1. Math and units
2. Scientific notation
3. Unit conversion
4. Accuracy
5. Precision
6. Significant figures
1. Units
and
Measurement
Physics
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
– 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 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
Conversion
• Example: Convert 5km to m:
• Multiply the original measurement by a
conversion factor.
NEW UNIT
85km x 1,000m = 85,000m
1km
OLD UNIT
14. Factor-Label Method of Unit
Conversion: Example
• Example: Convert 789m to km:
789m x 1km =0.789km= 7.89x10-1km
1000m
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
measured.
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
21.
22. Example: Evaluate whether the
following are precise, accurate or
both.
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
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
figs.
• 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
figs.
• 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
unknown.
– Substitute the knowns with units in the equation and