Dimensional Analysis
Dimensional analysis is a powerful tool for converting units within and between measuring systems. Keeping track of the 'units' in an equation assures some confidence in the numeric outcome.
Conversion factors come from basic relationships such as:
| English | 12 inches = 1 foot | 3 feet = 1 yard | 5280 ft = 1 mile |
| SI system | 1 km = 1000 m | 1m = 100 cm | 1 cm = 10 mm |
| English to SI system | 1 inch = 2.54 cm | 1 pound = 454 g | 1 quart = .95 liters |
From these a conversion factor can be created that is used in the original problem to obtain the units desired.
English units:
| 12 inches | 1 foot | 1 yard | 3 feet | 5280 ft | 1 mile |
| 1 foot | 12 inches | 3 feet | 1 yard | 1 mile | 5280 ft |
SI units:
| 1000 m | 1 km | 1 m | 100 cm | 1000 mm | 1 cm | 10 mm |
| 1 km | 1000 m | 100 cm | 1 m | 1 m | 10 mm | 1 cm |
English to SI units:
| 1 inch | 1 pound | 1 quart | 100 cm | 1000 mm | 1 cm | 10 mm |
| 2.54 cm | 454 g | .95 liters | 1 m | 1 m | 10 mm | 1 cm |
Example of an English system single conversion:
| 108 inches = ?? feet | 108 in | x | 1 foot | = | ______ feet |
|---|---|---|---|---|---|
| 12 in | |||||
| units 'cancel' | 108 |
x | 1 foot | = | ______ feet |
| 12 |
|||||
| evaluate | 108 | x | 1 foot | = | 9 feet |
| 12 |
Example of a SI unit double conversion:
| 2.47 km = ?? mm | 2.47 km | x | 1000 m | x | 1000 mm | = | ______ mm |
|---|---|---|---|---|---|---|---|
| 1 km | 1 m | ||||||
| units 'cancel' | 2.47 |
x | 1000 |
x | 1000 mm | = | ______ mm |
| 1 |
1 |
||||||
| evaluate | 2.47 | x | 1000 | x | 1000 mm | = | 2,470,000 mm |
| 1 | 1 |