1.3. Unit Conversions http://www.ck12.org
Examples Using Unit Conversions
Note: Answers to the illustrative examples below will be expressed inscientific notation. A number expressed in
scientific notation is written as a number between 1 and 10 multiplied by a power of ten. For example: 12, 300 =
- 23 × 104.
Illustrative Examples
For our purposes, let us regard the statement 1 km = 1000 m as an “equation.”
- How many meters are there in 10 km?
Answer:First we need aconversion factor. We know that 1 km = 1000 m. Dividing both sides by 1000 m,
1 km
1000 m=1, or equivalently1000 m
1 km =1.
The first result is useful if we wish to convert meters to kilometers, and the second result is useful if we wish to
convert kilometers to meters. Using this conversion factor, we put the units that we want on the top. Since the result
is in meters, we must convert from km to m. We use the unit conversion factor^10001 kmm.
10km×^10001 kmm= 10 ,000 m= 1 × 104 m
- Convert 10 m to km.
Answer:Here we use the conversion factor 10001 kmm.
(10 m)
(
1 km
1000 m)
=^1100 km= 0 .01 km= 1 × 10 −^2 km- Convert 100 km/h to m/s.
Answer:Recall that 1 h = 60 min = 3600 s.
(
100 km
1 h
)(
1000 m
1 km)(
1 h
3600 s)
= 27. 77 = 27 .8 m/sCheck Your Understanding
- Convert 60 mph (mi/h) to ft/s.
Answer:
Given: 5280 ft = 1 mile
(
60 mi
1 h
)(
5280 ft
1 mi)(
1 h
3600 s)
=88 ft/s- Convert 80 mg to kg.
Answer:(80 mg)
( 1 g
1000 mg)( 1 kg
1000 g)
= 8 × 10 −^5 kg- Convert 60.0 mi/h to m/s, given 1.609 km = 1.00 mi
Answer:
(
60. 0 mi
1. 00 h)(
1. 609 km
1. 00 mi)(
1000 m
1. 00 km)(
1. 00 h
3600 s)
= 26 .8 m/s= 26. 8 × 101 m/s