Using the Conversion Factor

Objective: Make unit conversions

Fill in the Missing Numbers

1 foot = _____ inches

1 meter = _____ centimeters

1 pound = _______ ounces

1 minute = ______ seconds

1 hour = ________ minutes

1 day = __________ seconds

12

100

16

60

60

86,400

Unit conversion factor

A unit conversion factor is a fraction whose numerator and denominator are equivalent measures. Some common unit conversion factors are given below. You can also use the reciprocal of these.

Choose a unit conversion factor that…

• Introduces the unit you want in the answer

• Cancels out the original unit so that the one you want is all that is left.

“Canceling” out Words

inches feet

feet miles

seconds hours

minutes seconds

inches

miles

hours

minutes

Convert 8 yards to feet…

Make a decision: What conversion factor will you use?

3 ft 1 yd or

1 yd 3 ft

Set up the problem: Multiply the measurement by the conversion factor.

ft yd

1 yd

38

Solve the problem: Perform the multiplication

ft yd ft ft yd ft

1 yd 1 yd

3 8 3 248 24

1 1

8 yards

1

A bucket holds 16 quarts. How many gallons of water will fill the bucket? Use a unit conversion factor to convert the units.

What are the two conversion factors comparing quarts and gallons?

4 qt

1 gal

1 gal

4 qt

Which one will “cancel” quarts?

16 qt 16 gal 4 gal

4

You Try it!One bag of apples weighs 64 ounces. How many pounds does it weigh?

1 lb 64 1 lb64 oz = 4 lb

16 oz 16

Darren drank 2 liters of water. How many milliliters of water did he drink?

1000 mL 2 1000 mL2 L = 2000 mL

1 L 1 L

Making Rate Conversions

Use a unit conversion to convert the units within each rate

Convert 80 miles per hour to feet per hour.

80 mi

1 hr

5,280 ft

1 mi

80 5280 ft

1 hr

422,400 ft

1 hr

Convert 63,360 feet per hour to miles per hour.

63,360 ft

1 hr

1 mi

5280 ft 63,360 ft 1 mi

1 hr 5280 ft

12 mi

1 hr

You Try it!Convert 32 feet per second to inches per second.

32 ft 12 in 32 ft 12 in 384 ft =

1 s 1 ft 1 s 1 ft 1 s

A craft store charges $1.75 per foot for lace. How much per yard is this?

$1.75 3 ft $1.75 3 ft $5.25 =

1 ft 1 yd 1 ft 1 yd 1 yd

Word Problems

The average American eats 23 pounds of pizza per year. Find the number of ounces the average American eats per year.

23 lb 16 oz 23 16 368 oz

1 yr 1 lb 1 1 yr

The average American eats 368 ounces of pizza per year.

Word Problems…A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? Hint: Set up the words first.

mi

hr

ft

mi

hr

s

How many seconds in an hour?

60 s 60 min 3600 s

1 min 1hr 1 hr

1 hr

3600 s

60 mi

2 hr

5,280 ft

1 mi

60 5,280

2 3600

44 ft

1 s

The car traveled 44 feet per second.