Steps to Converting Units (Dimensional Analysis)
1. Read the problem CAREFULLY. Then, re-read it CAREFULLY.
A car travels 5.8x108cm. How far is that in miles?
2. Identify the given quantity and the units of that quantity.
Δx = 5.8x108cm
3. Identify the wanted quantity, and the units of that quantity. Unless the problem states otherwise, you can assume
that the units for the wanted quantity are the base units for that quantity (seconds, meters, liters, kilograms).
Δx in miles
4. Determine a unit conversion path.
𝑐𝑚 ∙
𝑚 𝑓𝑡 𝑚𝑖
∙ ∙
= 𝑚𝑖
𝑐𝑚 𝑚 𝑓𝑡
5. Write all equivalences that you will need to complete the unit conversion path.
1 cm=10-2 m, 1 m=3.28ft, 5280 ft=1 mi
6. Use equivalences to create conversion factors that match your unit conversion path. Substitute them in.
5.8𝑥108 𝑐𝑚 ∙
10−2 𝑚 3.28𝑓𝑡 1𝑚𝑖
∙
∙
= ___________𝑚𝑖
1𝑐𝑚
1𝑚 5280𝑓𝑡
7. Cancel units to check that your unit path is correct.
5.8𝑥108 𝑐𝑚 ∙
10−2 𝑚 3.28𝑓𝑡 1𝑚𝑖
∙
∙
= ___________𝑚𝑖
1𝑐𝑚
1𝑚 5280𝑓𝑡
8. Multiply the numerators. Multiply the denominators. Divide the resulting fraction
10−2 𝑚 3.28𝑓𝑡 1𝑚𝑖
1.9024𝑥107
5.8𝑥10 𝑐𝑚 ∙
∙
∙
=
𝑚𝑖 = 3.603𝑥103 𝑚𝑖
1𝑐𝑚
1𝑚 5280𝑓𝑡
5280
8
9. Check significant figures, units, and scientific notation. Circle or box final answer
5.8𝑥108 𝑐𝑚 ∙
10−2 𝑚 3.28𝑓𝑡 1𝑚𝑖
1.9024𝑥107
∙
∙
=
𝑚𝑖 = 3.603𝑥103 𝑚𝑖 = 3.6𝑥103 𝑚𝑖
1𝑐𝑚
1𝑚 5280𝑓𝑡
5280
Measurement Conversion Chart
Distance
Weight
Volume
1 inch =
2.54 cm
1 ounce = 28.4 grams 1 teaspoon = 4.9 milliliters
1 foot = 0.328 meters 1 pound = 0.5 kilograms 1 cup = 237 milliliters
1 yard = 0.984 meters
1 pint = 473 milliliters
1 mile = 1.6 kilometers
1 quart = 0.9 liters
1 gallon = 3.79 liters