Metric Prefixes
Meaning
1012
109
6
10
103
Name
TeraGigaMegakilo-
Abbreviation
T
G
M
k
Meaning
10–2
10–3
–6
10
10–9
Name
Abbreviation
centic
milli- m
micro- µ
nano- n
These are the most commonly used metric
prefixes. You should commit them to memory.
Unit Conversions
In solving mathematical equations that contain
measurements, it is necessary that all the units of
measurement be consistant. For example, one should not
mix centimeters and meters within the same calculation.
An easy way to make the necessary conversions is to
use the powers of 10 notation.
6.7 km = 6.7 ✕ 103 m
In this way, all the measurements of length
within the same problem can be expressed in
terms of “meters”.
Unit Consistency
All of these conversions become possible with a working
knowledge of the meanings of the metric prefixes
–2
8.7 cm = 8.7 ✕ 10 m
–9
–7
756 nm = 756 ✕ 10 m = 7.56 ✕ 10 m
1300 kg = 1300 ✕ 103 m = 1.3 ✕ 106 m
980 cm/s2 = 980 ✕ 10–2 m/s2 = 9.8 m/s2
Relationships between units
“There are 100 centimeters in a meter.”
“There are 4 quarts in a gallon.”
These common expressions can be written
mathematically.
100 cm = 1 m
4 qt. = 1 gallon
Conversion Factors
They can also be written as ratios.
1m
100 cm
or
100 cm
1m
1 gallon
4 quarts
or
4 quarts
1 gallon
Which way you write them depends upon what
you want to do with them.
Conversion Factors in Use
Here's a sample problem that makes use of such a
conversion factor:
Problem: Convert 7.5 meter to centimeters.


100 cm
7.5 m
=750 cm
1m
In this case, we write “1 m” in the denominator
because we wish to cancel the units “m” and replace
them with “cm”.
Conversion Factors in Use
Here's another sample problem:
Problem: Convert 5.0 centimeters to meters.


1m
5.0 cm
=0.050 m
100 cm
In this case, we write “100 cm” in the denominator
because we wish to cancel the units “cm” and replace
them with “m”.
Conversion Factors in Use
Problem: Convert 9.2 millimeters to centimeters.


1 cm
9.2 mm
=0.92 cm
10 mm
“10 mm” appears in the denomenator because there
are 10 mm in one centimeter. The overall value of any
conversion factor is unity because whatever is written
in the numerator is equivalent to what is in the
denominator.
Converting Non-metric Units
Problem: Convert 672 seconds to minutes.


1 min
672 s
=11.2 min
60 s
If you accidently write the conversion factor the wrong way,
the units won't cancel and the answer looks rediculous.
672 s  160mins =40320 min
But 672 seconds ≠ 40320 minutes!
More Examples
Problem: Convert 11 feet to inches.


12 in
11.0 ft
=132 in
1 ft
Problem: Convert 180 sq. feet to sq. yards.

2
1 yd
180 ft 
2
9 ft
2
=20 yd
2
Metric ⇔ English Conversions
Problem: Convert 16 inches to centimeters.


2.54 cm
16.0 in
=40.6 cm
1 in
Problem: Convert 895 Watts to horsepower.


1 hp
895 Watts
=1.20 hp
745.7 Watts
Multiple Conversions
You may insert as many conversion factors as
necessary to complete the job.
Problem: Convert 4 days to seconds.

24 hours
4 days
1 day

60 min
1 hour


60 s
=345600 s
1 min
First we had to convert the days to hours, then the hours
to minutes, and finally the minutes to seconds.
In each step we had to cancel the previous units and
replace them with the next.
Multiple Conversions
In this example, we have to convert pre-existing
units in both the numerator and denominator.
Problem: Convert 105 km/h to m/s.

km
105
h

1000 m
1 km

1h
60 min


1 min
m
=29.2
s
60 s
Notice that the first conversion factor changes “km” to “m”.
Then the second and third conversion factors change the
“hours” to “minutes” and then to “seconds”.
Step-by-step
Let's go thorugh a converison problem one step at a
time to make sure we know what we're doing.
Problem: Convert 5030 joules to Btu's.
Step 1: Look up the conversion if you don't
know it or are unsure.
1 Btu = 1055 joules according to the list of
conversion factors found inside the front cover of the
text Physics by Cutnell and Johnson.
Step-by-step
Problem: Convert 5030 joules to Btu's.
Step 2: Write the conversion as a ratio. You
will decide later which version of the ratio
you will actually use.
1 Btu
1055 joules
or
1055 joules
1 Btu
Step-by-step
Problem: Convert 5030 joules to Btu's.
Step 3: Write the value you are given
followed by an empty set of parentheses into
which you will place your conversion factor.
(5030 joules)
(
)
=
Step-by-step
Problem: Convert 5030 joules to Btu's.
Step 4: Place the correct version of your ratio
within the parentheses so that the units you
want to change are cancelled.
(
)
1 Btu
(5030 joules)
1055 joules
=
Step-by-step
Problem: Convert 5030 joules to Btu's.
Step 5: Do the math. Write the answer with
the correct units.
(
)
1 Btu
(5030 joules)
1055 joules
= 4.77 Btu
Summary
Step 1: Look up the numerical value of the conversion you need.
Step 2: Write the conversion as a ratio.
Step 3: Write the value you are given followed by an empty
set of parentheses into which you will place your
conversion factor.
Step 4: Place the correct version of your ratio within the
parentheses so that the units you want to change are
cancelled.
Step 5: Do the math. Write the answer with the correct units.
(
)
1 Btu
(5030 joules)
1055 joules
= 4.77 Btu