Converting units with exponents has a myriad of practical uses, such as determining the amount of carpet required to cover a room. Often when converting units with exponents, you’ll solve problems involving units of area, such as square inches, square feet and square yards. The need may also arise to convert between units of volume, such as cubic inches, cubic feet and cubic yards.

The Facts

A unit with an exponent of two, such as 66 feet^2, is a square unit. Square units are two-dimensional measurements used to measure area, as in a floor plan. Units with exponents of three, such as 5 yards^3, are known as cubic units. Cubic units measure volume, a three-dimensional space such as a the inside of a swimming pool or milk carton.

Area: Converting Larger to Smaller Units

To convert a larger unit of area such as yards^2 to a smaller unit of area such as feet^2, multiply the number being changed by the conversion factor twice. For example, suppose you want to convert 7 yards^2 to feet^2. There are 3 feet in a yard, so multiply seven by three once to get 21, and then multiply 21 by three, resulting in an answer of 63 square feet, or 63 feet^2.

Area: Converting Smaller to Larger Units

When converting a smaller measurement of area, like inches^2, to a larger measurement of area, like feet^2, divide by the conversion factor twice. For instance, to change 216 inches^2 to feet^2, divide by twelve twice, since there are 12 inches in a foot. Step-by-step, 216 divided by 12 equals 18, and 18 divided by 12 produces 1.5. So, there are 1.5 square feet in 216 square inches.

Volume: Converting Larger to Smaller Units

Multiply by the conversion factor three times when converting a larger measure of volume to a smaller measure of volume, such as when converting feet^3 to inches^3. For example, suppose a question asks, “How many cubic inches are in 5 feet^3?” Since the conversion factor is 12 inches per foot, multiply three times, as follows: 5 x 12 = 60, 60 x 12 = 720, 720 x 12 = 8640. Hence, the answer to the question is that there are 8640 inches^3 in 5 feet^3.

Volume: Converting Smaller to Larger Units

To convert a smaller unit of volume, such as feet^3, to a larger unit of volume, such as yards^3, divide by conversion factor three times. Suppose you need to convert 108 feet^3 to yards^3. Since there are 3 feet in a yard, divide 108 by three to get 36, then divide 36 by 3 to produce 12, and lastly divide 12 by three, which gives a solution of 4 cubic yards.