Thursday, April 20, 2023

Unit Multipliers/Dimensional Analysis(Saxon) (Glencoe)

Converting units by using using unit multipliers (which is

dimensional analysis)

Compute mentally:

What are units?

Units-- the words we attach to numbers.

Examples: 3 feet 10 inches 5 meters

Denominate number -- the number

Units -- the word

What are units?

Write the units on your white board.

4 yards

8 miles per hour

5,280 feet

U.S. Customary System

The basic units of measure we use for length are related in the following ways:

12 inches = 1 foot3 feet = 1 yard

5,280 feet = 1 mile

You should memorize these!

U.S. Customary System

The basic units of measure we use for weight are related in the following ways:

16 ounces = 1 pound

2,000 pounds = 1 ton

You should memorize these!

What happens if you multiply something by a fraction that equals 1?

What would number would make each fraction equal to 1?

Unit Multipliers

Unit Multipliers can be written two ways.

Using Unit Multipliers

•

Unit multiplier

•

Unit multiplier

5 ft 12 in 1 1 ftNotice that the units “ft” cancel.

Yes, you can think this through without a unit multiplier. “I know there are 12 inches in every foot, so if I have 5 feet I will have 5 times 12 inches.

However, for this assignment, USE unit multipliers.And…SHOW YOUR WORK!!!!!!!!!!!!

• = 60 inches

Another example:

•

•

•

What if?

What if we had used the unit multiplier with yards on the bottom?

420 ft 3 ft

1 1 yd • = 1260 ft • ft

1 yd

Your Turn on the White BoardUse a unit multiplier to convert 72 inches

to feet.

Answer: 6 ft

Your Turn on the White BoardUse a unit multiplier to convert 4.6 miles to feet.

Answer: 24,288 ft

Your Turn on the White BoardUse a unit multiplier to convert 4 tons to pounds.

Answer: 8000 lb

Classwork Time

• Show your work with unit multipliers even if you can convert these in your head.

x

What you have

(number and units)

Units you have

Units you desire

1