2.1Measuring Lengths

Customary Units

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• Inch – length of a small paper clip

• Foot – distance from elbow to knuckle (12 inches)

• Yard – width of a door (3 feet)

Metric Units

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• Millimeter –width of a ship won (gold ship wons or penny)

• Centimeter – width of your little finger

• Meter height of a chair

Activity – Do This

• Measure how long your book is in paperclips.

height

width

Math Text Book

• A paper clip is about 1 inch long. About how long is your textbook.

Activity – Do This

• Using your finger tips, estimate the width of your book.

EXAMPLE 1 Using Customary Units of Length

EXAMPLE 1

Find the length of the caterpillar to the nearest inch

Using Customary Units of Length

EXAMPLE 1 Using Customary Units of Length

Find the length of the caterpillar to the nearest inch

EXAMPLE 1 Using Customary Units of Length

ANSWER

EXAMPLE 1 Using Customary Units of Length

Find the length of the caterpillar to the nearest inch

ANSWER

The caterpillar is about 2 inches long.

EXAMPLE 1 Using Customary Units of Length

Find the length of the caterpillar to the nearest inch

EXAMPLE 2 Using Metric Units of Length

EXAMPLE 2 Using Metric Units of Length

Find the length of the seashell to the nearest millimeter.

EXAMPLE 2 Using Metric Units of Length

Find the length of the seashell to the nearest millimeter.

EXAMPLE 2 Using Metric Units of Length

ANSWER

Find the length of the seashell to the nearest millimeter.

EXAMPLE 2 Using Metric Units of Length

ANSWER

The seashell is about 45 millimeters long.

Find the length of the seashell to the nearest millimeter.

EXAMPLE 3 Choosing Appropriate Tools

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

a. width of a calculator

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

a. width of a calculator b. length of a bus

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

a. width of a calculator b. length of a bus

SOLUTION

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

a. width of a calculator b. length of a bus

The width of a calculator is less than one foot and less than 30 centimeters.So, you should use a foot ruler or a centimeter ruler to measure the length.

SOLUTION

a.

EXAMPLE 3 Choosing Appropriate Tools

Choose an appropriate measuring tool for the length. Explain your reasoning.

The width of a calculator is less than one foot and less than 30 centimeters.So, you should use a foot ruler or a centimeter ruler to measure the length.

SOLUTION

a. width of a calculator

The length of a bus is greater than one yard and greater than one meter.So, you should use a tape measure to measure the length.

b. length of a bus

b.

a.

EXAMPLE 4 Choosing Appropriate Units

EXAMPLE 4 Choosing Appropriate Units

Choose an appropriate customary unit and metric unit for the length. Explain your reasoning.

EXAMPLE 4 Choosing Appropriate Units

a. distance from Boston to Chicago

Choose an appropriate customary unit and metric unit for the length. Explain your reasoning.

EXAMPLE 4 Choosing Appropriate Units

a. distance from Boston to Chicago

b. height of a full grown tree

Choose an appropriate customary unit and metric unit for the length. Explain your reasoning.

EXAMPLE 4 Choosing Appropriate Units

The distance from Boston to Chicago is much greater than one yard and much greater than one meter. So, use miles or kilometers.

SOLUTION

a.

EXAMPLE 4 Choosing Appropriate Units

The distance from Boston to Chicago is much greater than one yard and much greater than one meter. So, use miles or kilometers.

SOLUTION

The height of a tree is much greater than either one inch or one centimeter. The height is also much less than either one mile or one kilometer. So, use feet, yards, or meters.

b.

a.

EXAMPLE 5 Estimating Length Using Benchmarks

EXAMPLE 5

Estimate the height, in meters, of the door below. Measure to check.

Estimating Length Using Benchmarks

EXAMPLE 5

Estimate the height, in meters, of the door below. Measure to check.

STEP 1 To estimate, imagine how high the door is in “chairs.”

Estimating Length Using Benchmarks

EXAMPLE 5

Estimate the height, in meters, of the door below. Measure to check.

STEP 2 To check your estimate, measure the door with a meterstick.

Estimating Length Using Benchmarks

STEP 1 To estimate, imagine how high the door is in “chairs.”

ANSWER

EXAMPLE 5

Estimate the height, in meters, of the door below. Measure to check.

STEP 2 To check your estimate, measure the door with a meterstick.

Estimating Length Using Benchmarks

STEP 1 To estimate, imagine how high the door is in “chairs.”

ANSWER

EXAMPLE 5

Estimate the height, in meters, of the door below. Measure to check.

STEP 2 To check your estimate, measure the door with a meterstick.

The door is about 2 “chairs” high, which is about 2 meters. The height of the door is just over 2 meters.

Estimating Length Using Benchmarks

STEP 1 To estimate, imagine how high the door is in “chairs.”