Dimensional Analysis WS
Conversion Factors: Fill in the blank for each conversion factor.
1 week = ________ days
1 pint = ________ cups
365 days = ________ years
1 mL = ________ cm3
4 quarts = ________ gallons
1 mile = ________ feet
2.54 centimeters = ________ inces
60 seconds = ________ minutes
12 inches = ________ foot
1 day = ________ hours
1 quart = ________ pints
1 cup = ________ tablespoons
One Step Problems: Using the conversion factors above, make ratios to solve the following problems. Remember to
stack the ration so the given units cancel and the desired unit is left.
20 𝑤𝑒𝑒𝑘𝑠 (
) = __________𝑑𝑎𝑦𝑠
5 𝑐𝑢𝑝𝑠 (
) = __________𝑝𝑖𝑛𝑡𝑠
272 𝑑𝑎𝑦𝑠 (
) = __________𝑦𝑒𝑎𝑟𝑠
15 𝑐𝑚3 (
) = __________𝑚𝐿
1.6 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 (
6 𝑖𝑛𝑐ℎ𝑒𝑠 (
39 𝑖𝑛𝑐ℎ𝑒𝑠 (
) = __________𝑞𝑢𝑎𝑟𝑡𝑠
590 𝑓𝑒𝑒𝑡 (
) = __________𝑐𝑚
400 𝑠𝑒𝑐 (
) = __________𝑓𝑒𝑒𝑡
30 𝑑𝑎𝑦𝑠 (
) = __________𝑚𝑖𝑙𝑒𝑠
) = _________𝑚𝑖𝑛𝑠
) = __________ℎ𝑜𝑢𝑟𝑠
Multiple Step Problems: a number can be multiplied by several conversion factors in a row to do a more complex
conversion. Solve these problems and show all work. Start with the given number and be sure to cancel out all units
until you get the desired units.
How many seconds in 1 year?
1 𝑦𝑒𝑎𝑟 (
)(
)(
)(
) = _________________𝑠𝑒𝑐𝑜𝑛𝑑𝑠
How many kilometers in 1 mile? (use knowledge of metric conversions too)
1 𝑚𝑖𝑙𝑒 (
)(
)(
)(
) = _________________𝑘𝑚
If you have 2.0 days to complete an assignment, how many seconds is that?
2 𝑑𝑎𝑦𝑠 (
)(
)(
) = _________________𝑠𝑒𝑐𝑜𝑛𝑑𝑠
Now set the problems up without the parentheses given for each conversion. Again be sure to to cancel out all
units until you get the desired unit.
If an Oreo cookie is 0.654 cm thick (1 cookie = 0.654 cm), how many Oreos does it take to reach the moon if the
moon is 3.84 x 108 m away from the Earth? (start with 3.84 x 108m)
If a penny is 1.15 mm thick (1 penny = 1.15 mm), how many pennies are needed to reach the ceiling in a room where
the height is 2.30 m?
If I were to drive to Vancouver Canada from here, it is 2530 km. How far is it in mm? How about miles?
How long in days would it take me to drive if I went an average speed of 90km/hr and drove 13 hours per day?
(start with 5200 km  hours  days)
A blacksmith has to put new shoes on a stable of horses. Each shoe requires 3 nails. How many nails must be
brought to the stable if there are 20 horses?
You need to adapt a cookie recipe for a family reunion. One recipe makes 2 dozen cookies, and it calls for 2
teaspoons (2 t) of baking soda. How many cups of baking soda will you need to make 60 dozen cookies? Report your
answer to the nearest ¼ of a cup. (3 teaspoons (t) = 1 tablespoon (T); 16 T = 1 cup
How many teaspoons of water are in 5.00 gallons?