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Dimensional Analysis. Honors Math – Grade 7. Conversion Factors. 1 liter (L) = 100 centiliters (cL) 1 L = 33.82 fluid ounces (fl oz) 1 serving = 5 fl oz. Problem of the Day.

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dimensional analysis

Dimensional Analysis

Honors Math – Grade 7

slide2

Conversion Factors

1 liter (L) = 100 centiliters (cL)

1 L = 33.82 fluid ounces (fl oz)

1 serving = 5 fl oz.

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.

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

slide3

Conversion Factors

1 liter (L) = 100 centiliters (cL)

1 L = 33.82 fluid ounces (fl oz)

1 serving = 5 fl oz.

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

Start with what is given – 150 cL.

Use conversion factors to cancel.

Cancel like units.

Multiply numerators & denominators. Then divide.

slide4

Conversion Factors

Conversion Factors

1 qt = 0.946 L

1 lb = 454 g

Use dimensional analysis to rename each unit of measure.

slide5

Conversion Factors

1 yd3 = 27 ft3

Use dimensional analysis to rename each unit of measure.

slide6

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?