Representing, Comparing, Ordering, and Estimating Decimals#8

Place value can help you understand and write and compare decimal numbers.

Vocabulary

Example 1: Reading and Writing Decimals

Write each decimal in standard form, expanded form, and words.

A. 1.07

B. 0.03 + 0.006 + 0.0009

Example 2: Reading and Writing Decimals

Write the decimal in standard form and expanded form.

C. fourteen and eight hundredths

Example 3: Real-World Application

The star Wolf 359 has an apparent magnitude of 13.5. Suppose another star has an apparent magnitude of 13.05. Which star has the smaller magnitude?

Example 4: Real-World Application

Marci shipped two packages. One weighed 7.231 pounds and the other weighed 7.229 pounds. Which package weighed less?

Additional Example 5: Comparing and Ordering Decimals

Order the decimals from least to greatest.

16.67, 16.6, 16.07

Example 5 Continued

Graph the numbers on a number line.

16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17

Example 6: Comparing and Ordering Decimals

Order the decimals from greatest to least.

0.08, 0.04, 0.1

Example 6 Continued

Graph the numbers on a number line.

0 0.02 0.04 0.06 0.08 0.10

Example 7

Order the decimals 12.42, 12.4, 12.02 from least to greatest.

12.42, 12.4, 12.02

12 12.1 12.2 12.3 12.4 12.5

When numbers are about the same value, you can use clustering to estimate. Clustering means rounding the numbers to the same value.

Vocabulary

Example 8: Real-World Application

Nancy wants to cycle, ice skate, and water ski for 30 minutes each. About how many calories will she burn in all? (Cycling = 165.5 calories, ice skating = 177.5 calories, and water skiing = 171.5 calories)

Example 9

Abner wants to run, roller-skate, and snow ski for 60 minutes each. About how many calories will he burn in all? (Running = 185.5 calories, roller-skating = 189.5 calories, and snow skiing = 191.5 calories.)

Look at the digit to the right of the place to which you are rounding.

• If it is 5 or greater, round up.

• If it is less than 5, round down.

Caution!

Example 10: Rounding Decimals to Estimate Sums and Differences

Estimate by rounding to the indicated place value.

A. 7.13 + 4.68; ones

B. 9.705 – 0.2683; tenths

Example 11: Using Compatible Numbers to Estimate Products and Quotients

Estimate each product or quotient.

A. 33.83 1.98

B. 72.77 ÷ 26.14

You can also use front-end estimation to estimate with decimals. Front-end estimation means to use only the whole-number part of the decimal.

Vocabulary

Additional Example 12: Using Front-End Estimation

Estimate a range for the sum.

7.86 + 36.97 + 5.40

Use front-end estimation.

Example 13

Estimate a range for the sum.

8.92 + 47.88 + 3.41