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 expresses a basic relationships between units:
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 
2.54 cm  454 g  .95 liters 
Process
 Place desired units on the right of the equals sign.
 Place the given units to the left of the equals.
 Select the denominator of the conversion factor so that it has the same units as the given unit.
 Select the numerator of the conversion factor so that it has the same units as the desired unit.
 Insert the actual numbers appropriate for the conversion factor.
 The given unit and the conversion factor unit will "cancel", leaving just the desired unit.
 Complete the indicated multiplication.
Example 1
Example of an English system single conversion: 108 inches = ?? feet
 Place desired units on the right of the equals sign.
x = ______ feet  Place the given units to the left of the equals.
108 inches x = ______ feet  Select the denominator of the conversion factor so that it has the same units as the given unit.
108 inches x = ______ feet inches  Select the numerator of the conversion factor so that it has the same units as the desired unit.
108 inches x foot = ______ foot inches  Insert the actual numbers appropriate for the conversion factor.
108 inches x 1 foot = ______ feet 12 inches  The given unit and the conversion factor unit will "cancel", leaving just the desired unit.
108 inchesx 1 foot = ______ feet 12 inches  Complete the indicated multiplication
108 x 1 foot = 9 feet 12
Example 2
Example of an English to SI system single conversion: 3 pounds = ?? grams
 Place desired units on the right of the equals sign.
x = ______ grams  Place the given units to the left of the equals.
3 pounds x = ______ grams  Select the denominator of the conversion factor so that it has the same units as the given unit.
3 pounds x = ______ grams pounds  Select the numerator of the conversion factor so that it has the same units as the desired unit.
3 pounds x grams = ______ grams pounds  Insert the actual numbers appropriate for the conversion factor.
3 pounds x 454 grams = ______ grams 1 pound  The given unit and the conversion factor unit will "cancel", leaving just the desired unit.
3 poundsx 454 grams = ______ grams 1 pounds  Complete the indicated multiplication
3 x 454 grams = 1362 grams 1
Example 3
Example of an English system double conversion: 1.2 miles = ?? inches
 Place desired units on the right of the equals sign.
x = ______ inches  Place the given units to the left of the equals.
1.2 miles x = ______ inches  Select the denominator of the conversion factor so that it has the same units as the given unit.
1.2 miles x = ______ inches miles  Select the numerator of the conversion factor so that it has the same units as the desired unit.
1.2 miles x inches = ______ inches miles  Insert the actual numbers appropriate for the conversion factor.

OOPS, we don't know a conversion from miles to inches.
1.2 miles x ? inches = ______ inches ? miles  We will have to add another conversion factor we do know.
1.2 miles x feet x = ___ inches miles  For the second conversion factor we must convert from feet to inches.
1.2 miles x feet x inches = ___ inches miles feet  Now we can add the approproaite numbers.
1.2 miles x 5280 feet x 12 inches = ___ inches 1 mile 1 foot

OOPS, we don't know a conversion from miles to inches.
 The given unit and the conversion factor unit will "cancel", leaving just the desired unit.
1.2 milesx 5280 feetx 12 inches = ___ inches 1 mile1 foot  Complete the indicated multiplication
1.2 x 5280 x 12 inches = 76,032 inches 1 1