Dimensional Analysis Vocabulary Unit conversion factor a fraction

* Dimensional Analysis

$Vocabulary Unit conversion factor- a fraction in which the numerator and denominator represent the$

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

Additional Example 1: Using Conversion Factors to Solve Problems The average American uses 580 pounds of paper year. Find this rate in pounds per month, to the nearest tenth. 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. yr lb lb Cancel yr units. yr • mo = mo Divide 580 by 12. The average American uses 48. 3 pounds of paper month.

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.

Additional Example 2: Converting Between Metric and Customary Units 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 miles kilometers 1 1. 6 x = 10 Write a proportion using 1 mi. = 1. 6 km. The cross products 1 · 10 = 1. 6 · x are equal. 10 = 1. 6 x ___ 1. 6 6. 25 = x Multiply. Divide each side by 1. 6. A 10 kilometer race is about 6. 3 miles.

Check It Out: Example 2 A 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 2 B One gallon is equal to about 3. 875 liters. How many liters are there in 6 gallons? Round to the nearest tenth.

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.