Unit Conversion Worksheet
When converting from one a unit to another it is useful to use conversion factors. Conversion factors are fractions that
equal 1 because the numerator (top) equals the denominator (bottom), but the top and bottom have different units. In
algebra you learned that multiplying any quantity by 1 does not change the quantity’s value, so we can use conversion
factors to change the units of a measurement without changing the value of the measurement.
For instance, we know 1 km = 1 (103)m, 1 min = 60 s, and 1 hr = 60 min. For each of these 3 equivalence statements we
can divide both sides by one of the two quantities to create the conversion factors below:
__1 km _ = 1
1000 m
or 1 = _1000m _
1 km
__1 min _ = 1 or 1 = _60 s _
60 s
1 min
__1 hr _ = 1
60 min
or 1 = _60 min _
1 hr
By using all 3 of these conversion factors you can convert 15 km/hr into m/s. Be careful to use the conversion factor
that cancels the units you are trying to convert out of. If you can cancel (reduce to 1) those units you did it correctly.
15 km
1000 m
1 hr
1 min
= 4.2 m/s
1 hr
1 km
60 min
60 s
When using prefixes like micro (µ), milli (m), kilo (k), giga (G), etc., make sure to “translate” the prefix’s meaning to the
other half of the conversion factor. Since µ = 10-6, 1µs = 1(10-6)s. So you can create the conversion factors 1µs / 10-6s
and 10-6s/1µs. But 10-6µs ≠ 1s, so be careful not to use 10-6µs/1s. Note: Prefixes can go with any unit (g, m, s, Hz, etc.)
Carry out the following conversions. If you have trouble, start by writing out the conversion factors you’ll need.
1. 1.00 year (non-leap year) into seconds.
2. 55g into kg.
3. 36 km into cm.
4. 22kg into mg
5. 5.00 m/s into mi/hr
6. 60.0 L into mL
7. 170 cm/min into m/s
8a. The speed of light (in a vacuum) is 3.0 x 108 m/s. Convert this speed into km/day and b) mi/hr.
8b. The speed of light (in a vacuum) is 3.0 x 108 m/s. Convert this speed into mi/hr.
9. 95kg = _____ g
10. 3.5cm= _____dam. (Note: da=deka, so dam = dekameters.)
11. 25 MHz = _____ Hz (Note: Don’t worry about what unit Hz is, you can still do the conversion.)
12. 343 m/s = _____ mi/hr
13. 32 ft/s2 = _____ m/s2 (Hint: Use 3 conversion factors. In your notes you have the conversion between in and cm.)
14. 1.013 x 105 N/m2 = _______ N/cm2 (Note: This happens to be a pressure of 1 atm also)
15. 230 g*cm2/s2 = _______ kg*m2/s2
16. 57.0 kg*km/min2=______ kg*m/s2
17. 1.0m/s is roughly 2.2mi/hr. Give a reasonalbe speed in m/s for
a. walking,
b. running,
c. a car on the freeway.