Physics 101: Chapter 1
Measurement Systems
Significant Figures
Dimensional Analysis
Physics 101: Chapter 1, Pg 1
Measurement Systems



SI – International System
US – British System
Basic Metric Units
Quantity Length Mass
Unit
meter kilogram
Symbol m
kg
Time
second
s
El. Current
Ampere
A
Temperature
Kelvin
K
Physics 101: Chapter 1, Pg 2
Si Prefixes
Power
10-18
10-15
10-12
10-9
10-6
10-3
103
106
109
1012
1015
1018
Prefix
atto
femto
pico
nano
micro
milli
kilo
mega
giga
tera
peta
exa
Symbol
a
f
p
n

m
k
M
G
T
P
E
Physics 101: Chapter 1, Pg 3
Metric Line
METRIC LINE
Tm
Tg
Tl
Gm
Gg
Gl
T - tera
G - giga
M - mega
k - kilo
m - milli
u - micro
n - nano
p - pico
f - femto
Mm
Mg
Ml
km
kg
kl
m
g
l
mm
mg
ml
um
ug
ul
nm
ng
nl
pm
pg
pl
fm
fg
fl
am
ag
al
Length
Mass
Capacity
Center
m - meter
g - gram
l - liter
Physics 101: Chapter 1, Pg 4
Conversion Table
METRIC TO ENGLISH
ENGLISH TO METRIC
From Metric
To English
Multiply by
From English
To Metric
Multiply by
meters
meters
centimeters
kilometers
grams
kilograms
liters
liters
yards
feet
inches
miles
ounces
pounds
quarts
gallons
1.09
3.28
0.39
0.62
0.035
2.20
1.06
0.26
yards
feet
inches
miles
ounces
pounds
quarts
gallons
meters
meters
centimeters
kilometers
grams
kilograms
liters
liters
0.91
0.30
2.54
1.61
28.35
0.45
0.95
3.78
Physics 101: Chapter 1, Pg 5
Temperature Conversion
Conversion of Fahrenheit to Celsius
5( F  32)
C
9
Conversion of Celsius to Fahrenheit
F
9C
 32
5
Physics 101: Chapter 1, Pg 6
Conversion into Metric

Example 1: Convert 50 mph to m/s.
From 1 mile = 1609 m:
50miles 1609m 1h
m


 22m
h
miles 3600 s
s

Example 2: A hall bulletin board has
an area of 2.5 m2. What is this area in
cm2?
Because 1m=100cm it is sometimes
assumed that 1 m2 = 100 cm2, which
is WRONG. The correct conversion is:
2.5m2  2.5m  m  2.5 100cm 100cm  25000cm2  2.5 104 cm2
Physics 101: Chapter 1, Pg 7
Significant Figures



The number of significant figures of a numerical quantity is the
number of reliably known digits it contains.
Zeros at the beginning of a number are not significant. They merely
locate the decimal point.
 0.254 - three significant figures (2, 5, 4)
Zeros within a number are significant
 104.6 - four significant figures (1, 0, 4, 6)
Zeros at the end of a number after the decimal point are significant:
 2705.0 - five significant figures (2, 7, 0, 5, 0)
Physics 101: Chapter 1, Pg 8
Significant Figures - Conclusion


The FINAL result of a multiplication or division should have the same
number of significant figures as the quantity with the least number of
significant figures that was used in the calculation.
The FINAL result of the addition or subtraction of numbers should
have the same number of decimal places as the quantity with the
least number of decimal places that was used in the calculation.
Physics 101: Chapter 1, Pg 9
Significant Figures - Practice

Example 1:
Find the area of a room 2.4 m by 3.65 m:
2.4m x 3.65m = 8.76m2=8.8m2
Rounded to 2 s.f. - because 2 is least # of s.f.

Example 2:
Given the numbers 23.25, 0.546, and 1.058
add the first two
subtract the least number from the first
Physics 101: Chapter 1, Pg 10
Dimensional Analysis




The two sides of an equation must be equal not only in numerical value, but also in
dimensions (BOTH SIDES OF THE EQUATION ARE NUMERICALLY AND
DIMENSIONALLY EQUAL). And dimensions can be treated as algebraic quantities.
[L] - Length
[M] - Mass
[T] - Time
Physics 101: Chapter 1, Pg 11
Dimensional Analysis - Practice

Example 1:
Is an equation x = v t
a correct equation?
x - is the distance in m
v = is the velocity in m/s
t - is the time in s

Example 2:
Is an equation x = a t2
a correct equation?
a is acceleration in m/s2
[ L] 
[ L]
2

[
T
]  [ L]
2
[T ]
Dimensionally the equation is:
[ L] 
[ L]
 [T ]  [ L]
[T ]
Physics 101: Chapter 1, Pg 12
Practice


Show that the equation
x = xo + vt,
where v is velocity, x and xo are
lengths, ant t is time, is
dimensionally correct.
A Boeing 777 jet has a length of
209 ft. 1 inch, and wingspan of
199 ft and 11 inches. What are
these dimensions in meters?

Determine the number of
significant figures:
 1.007 m
 8.03 m
 16.272 kg
 0.015 µs

The two sides of right triangle
are 8.7 cm (two significant
figures) and 10.5 cm (three
significant figures). What is the
area of the triangle?
Physics 101: Chapter 1, Pg 13