Dimensional Analysis

Honors Math – Grade 7

Problem of the Day

Ann drinks a 5-fluid-ounce serving of a rehydrating drink after each run. For how many runs will a 150-centiliter bottle of the drink last Ann?

What are the important facts?

To find how many runs, find out how many servings are in 150 cL using dimensional analysis.

Dimensional, or unit analysis is the process of analyzing units to decide which conversion factor(s) to use.

Conversion Factors1 liter (L) = 100 centiliters (cL)1 L = 33.82 fluid ounces (fl oz)1 serving = 5 fl oz.

Let’s take a closer look at how this works.

To use dimensional analysis: set up the conversion factors in a sequence so that like units cancel out through multiplication.

Conversion Factors1 liter (L) = 100 centiliters (cL)1 L = 33.82 fluid ounces (fl oz)1 serving = 5 fl oz.

150𝑐𝐿1

Start with what is given – 150 cL. Use conversion factors to cancel.

1𝐿100𝑐𝐿

33.82 𝑓𝑙𝑜𝑧1𝐿

1𝑠𝑒𝑟𝑣𝑖𝑛𝑔5 𝑓𝑙𝑜𝑧

Cancel like units. Multiply numerators & denominators. Then divide.

×××

150×1×33.82×1100×1×5

Use dimensional analysis to rename each unit of measure.

300 yd = ? in. 3.25 mi = ? in.

Conversion Factors1 qt = 0.946 L

Conversion Factors1 lb = 454 g

Use dimensional analysis to rename each unit of measure.

Conversion Factors1 yd3 = 27 ft3

Use dimensional analysis to solve the problem.

A gallon of water weighs 8.3 pounds. A cubic foot of water weighs about 623 pounds. To the nearest tenth, about how many gallons of water would fill a cubic ft?

The average respiratory rate for an adult is 16 breaths per minute. About how many times does an adult breath in one week? A year?