Unit Conversions
It is very important that you are easily able to convert quantities from one unit to another…45 km to mm, 3.5 E
-6 kg to g, etc. Here is a method that works to convert units. There are also some practice problems with
answers after the examples. You also need to be able to look up metric prefixes and know how to convert them.
Example #1: It is 4.2 miles to the airport. Convert this quantity to meters. (Note that “mi” means miles and “m”
means meters.)
Step 1. Write down the quantity you are given.
4.2 miles
Step 2. Write down the required conversion factor to change between units. Note that there are 2 forms of the
conversion factor and it doesn’t matter which one you use…as long as the correct units are on the bottom so that
they will cancel. Both ways are shown here.
4.2 𝑚𝑖𝑙𝑒𝑠 𝑥
1610 𝑚𝑒𝑡𝑒𝑟𝑠
1 𝑚𝑖𝑙𝑒
= 6762 meters
OR
4.2 𝑚𝑖𝑙𝑒𝑠 𝑥
1 𝑚𝑒𝑡𝑒𝑟
6.21 𝐸−4 𝑚𝑖𝑙𝑒𝑠
= 6763 meters
You will get slightly different answers when using conversion factors depending on how many digits you use.
Remember to check your final answer…a meter is smaller than a mile, so there should be lots of meters in 4.2
miles.
Example #2: Determine the number of seconds in one year. This requires multiple steps. Set up the
conversion factors as fractions one after another, being sure to have the units in the right location to cancel.
Then multiply all the numbers on top. Multiply all the number on the bottom, and then do the final calculation.
Step 1. Always start with the quantity you are given.
1 year
Step 2. Write down the conversion factors with the correct units on top/bottom.
𝟏 𝒚𝒆𝒂𝒓 𝒙
𝟑𝟔𝟓 𝒅𝒂𝒚𝒔
𝟏 𝒚𝒆𝒂𝒓
𝒙
𝟐𝟒 𝒉𝒐𝒖𝒓𝒔
𝟏 𝒅𝒂𝒚
𝒙
𝟔𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝟏 𝒉𝒐𝒖𝒓
𝒙
𝟔𝟎 𝒔𝒆𝒄𝒐𝒏𝒅𝒔
𝟏 𝒎𝒊𝒏𝒖𝒕𝒆
= 31536000 seconds = 3.15 E 7 seconds (3 sig figs)
Check the answer…lots of seconds in one year.
Example #3: The sun produces 386 YottaWatts. How many watts is that? For this problem you will have to
look up the conversion factor for the metric prefix “yotta”. For this class you will need to know the following
prefixes: milli, centi, kilo, mega.
Step 1: Start with the quantity you are given.
386 Yottawatts
Step 2: Look up the meaning of the prefix “yotta”….= 1024. You can do a direct substitution…whenever you
see “yotta”, replace it with “E 1024”. So 25 Yotta watts = 25 E 1024 watts. (Continued on next page.)
386 𝑌𝑜𝑡𝑡𝑎𝑤𝑎𝑡𝑡𝑠 𝑥
1 𝐸 24 𝑤𝑎𝑡𝑡𝑠
= 386 E 24 Watts
1 𝑦𝑜𝑡𝑡𝑎𝑤𝑎𝑡𝑡
Check the answer…lots of watts in one yottawatt.
Example #4: Change 35 milligrams to kilograms
Step 1: Start with the quantity you are given.
35 milligrams
Step 2: Using the meaning of the metric prefixes, first change milligrams to grams, then from grams to
kilograms. Metric prefixes are always defined relative to the base unit: meter, gram, etc.
“kilo” = 1 E 3, “milli” = 1 E -3
35 𝑚𝑔 𝑥
1 𝐸−3 𝑔𝑟𝑎𝑚𝑠
1 𝑚𝑔
𝑥
1 𝑘𝑔
1 𝐸 3 𝑔𝑟𝑎𝑚𝑠
=
35 𝐸− 3 𝑘𝑔
1𝐸3
= 35 E -6 kg = .0000035 kg
This number should make sense…a milligram is much smaller than a kilogram so the final answer will be less
than one.
Example #5: Convert 60 miles/hour to meters/second. Be careful when converting units in both the numerator
and denominator. Set up the unit conversions as fractions watching which units cancel.
Step 1: Start with the given quantity.
60 𝑚𝑖𝑙𝑒𝑠
ℎ𝑜𝑢𝑟
Step 2: Insert the conversion factors. Note how the conversion factors are set up for cancelling units.
60 𝑚𝑖𝑙𝑒𝑠
ℎ𝑜𝑢𝑟
𝑥
1610 𝑚𝑒𝑡𝑒𝑟𝑠
1 𝑚𝑖𝑙𝑒
𝑥
1 ℎ𝑜𝑢𝑟
60 𝑚𝑖𝑛𝑠
𝑥
1 𝑚𝑖𝑛
60 𝑠𝑒𝑐
=
96600 𝑚𝑒𝑡𝑒𝑟𝑠
3600 𝑠𝑒𝑐
Sample Problems…answers are at the end of all of the problems.
Do the following conversions:
1. 25 feet to meters
2. 12.0 inches to cm
3. 7.0 days to seconds
4. 1.00 km to feet
= 26.8 m/s
5. 200 miles to km
6. 150 pounds to kg
7. 5 feet 10 inches to cm
8. 3.52 E 6 kilojoules to joules
9. 0.00098 milliliters to liters
10. 25 square feet to square meters (be sure to square the conversion factors!)
11. Acceleration due to gravity = 32 feet/ second2 change to meters/second2
12. 30 miles/hour to meters/second
13. 750 microns (micrometer = ) to megameters (mega = M)
14. 850 kilohertz to centihertz (hertz are a measure of frequency)
15. density = 25300 grams/cm3 to kg/m3
Answers:
1) 7.6 m 2) 30.5 cm 3) 604800 sec 4) 3280 ft 5) 321.8 kkm 6) 67.5 kg 7) 177.8 cm 8) 3.52 E 9 Joules
9) 9.8 E-7 liters 10) 2.32 m2 11) 9.75 m/s2 12) 13.4 m/s 13) 7.5 E-10 Mm 14) 8.50 E7 cHz
15) 2.53 E 7 kg/m3