Dimensional Analysis

*Notes 41

Vocabulary

Unit conversion factor- a fraction in which the numerator and denominator represent the same quantity in different units.

The average American uses 580 pounds of paper per year. Find this rate in pounds per month, to the nearest tenth.

Additional Example 1: Using Conversion Factors to Solve Problems

The problem gives the ratio 580 pounds to 1 year and asks for an answer in pounds per month.

580 lb 1 yr

1 yr 12 mo

580 lb 12 mo

=

= 48.3 lb per month

Multiply the ratio by the conversion factor.

Divide 580 by 12.

The average American uses 48.3 pounds of paper per month.

Cancel yr units. •yrmo= lb

molbyr

Check It Out: Example 1

Sam drives his car 23,040 miles per year. Find this rate in the number of miles driven per month, to the nearest mile.

One mile is about 1.6 kilometers. What is the length in miles of a 10 kilometer race? Round to the nearest tenth of a mile.

Write a proportion using 1 mi. = 1.6 km.

= miles kilometers

1 1.6

Additional Example 2: Converting Between Metric and Customary Units

x 10

1 · 10 = 1.6 · xThe cross products are equal.

10 = 1.6x Multiply. ___ ___ 1.6 1.6 Divide each side by

1.6.6.25 = x

A 10 kilometer race is about 6.3 miles.

One inch is equal to 2.54 centimeters. How many inches are there in 12 centimeters? Round to the nearest tenth.

Check It Out: Example 2A

One gallon is equal to about 3.875 liters. How many liters are there in 6 gallons? Round to the nearest tenth.

Check It Out: Example 2B

Additional Example 3: Application

A tennis pro serves a ball that travels the length of the court, 78 feet, in 0.75 second. How fast is the ball moving in feet per second? Check your answer for reasonableness.

Additional Example 3 Continued

The ball’s speed is 104 ft/s.

Convert ft/s to mi/h to see if the answer is reasonable.

The ball’s average speed is 71 mi/h, which is a reasonable speed for a serve.

Check It Out: Example 3

Gary travels 1,320 ft in 1.5 min on his bicycle. How fast is he traveling in feet per min? Check your answer for reasonableness.