Chapter 3, Section 2, Page 98

“Estimating Decimals”

Warm UpOrder the decimals from least to greatest.

1. 18.74, 18.7, 18.47

2. 9.06, 9.66, 9.6, 9.076

Write each in words.3. 3.072

4. 6.1258

18.47, 18.7, 18.74

9.06, 9.076, 9.6, 9.66

three and seventy-two thousandths

six and one thousand two hundred fifty-eight ten-thousandths

MA.6.A.5.2 Estimate the results of computations with…decimals…and judge the reasonableness of the results.

Sunshine State Standards

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

Clustering means rounding the numbers to the same value.

Vocabulary You Need to Know

Compatible numbers are close to the numbers that are in the problem and are helpful when you are solving the problem mentally.

Example 1: Health 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)

165.5 170 The addends cluster around 170.

177.5 170 To estimate the total number of calories, round each addend to 170.

171.5 + 170

Add. 510

Nancy burns about 510 calories.

Check It Out: Example 1

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)

185.5 190 The addends cluster around 190.

189.5 190 To estimate the total number of calories, round each addend to 190.

191.5 + 190

Add. 570

Abner burns about 570 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!Caution!

5 or more,

raise the

score!

4 or less,

let it rest!

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

7.13 + 4.68 Round to the nearest whole number.

7 + 5 = 12 The sum is about 12.

9.705 9.7 Round to the tenths.

Align.

9.4 Subtract.

– 0.2683 –0.3

Example 2

Estimate by rounding to the indicated place value.

A. 6.09 + 3.72; ones

B. 8.898 – 0.4619; tenths

6.09 + 3.72 Round to the nearest whole number.

6 + 4 = 10 The sum is about 10.

8.898 8.9 Round to the tenths.

Align.

8.4 Subtract.

–0.4619 –0.5

Using Compatible Numbers to Estimate Products and Quotients

Estimate each product or quotient.

A. 33.83 1.98

B. 72.77 ÷ 26.14

35 2 = 70 35 and 2 are compatible.

75 ÷ 25 = 3 75 and 25 are compatible.

So, 72.77 ÷ 26.14 is about 3.

So 33.83 1.98 is about 70.

Example 3

Estimate each product or quotient.

A. 22.12 4.98

B. 62.31 ÷ 18.52

20 5 = 100 20 and 5 are compatible.

60 ÷ 20 = 3 60 and 20 are compatible.

So, 62.31 ÷ 18.52 is about 3.

So 22.12 4.98 is about 100.

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.

Using Front-End Estimation

Estimate a range for the sum.

7.86 + 36.97 + 5.40

Use front-end estimation.

7.86 7 Add the whole numbers only.

36.97 36 The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate.

5.40 + 5

at least 48

The exact answer of 7.86 + 36.97 + 5.40 is greater than 48.

Example 4 Continued

You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals up to 0.5 or 1.

0.86 1.00Add the adjusted decimal part of the numbers.

0.97 1.00 Add the whole-number estimate and this sum. 0.40 + 0.50

2.50

48.00 + 2.50 = 50.50

The adjusted decimals are greater than the actual decimal, so 50.50 is an overestimate.

The estimated range for the sum is from 48.00 to 50.50.

Example

Estimate a range for the sum.

8.92 + 47.88 + 3.41

Use front-end estimation.

8.92 8 Add the whole numbers only.

47.88 47 The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate.

3.41 + 3

at least 58

The exact answer of 8.92 + 47.88 + 3.41 is greater than 58.

Lesson Quiz

Estimate each product or quotient.

3

14

80 cm

3. 6.75 1.82

4. 10.5 ÷ 3.42

5. The snowfall in December, January, and February was 18.26 cm, 29.36 cm, and 32.87 cm, respectively. About how many total centimeters of snow fell during the three months?

Estimate by rounding to the indicated place value.

3

4.51. 3.07442 + 1.352; tenths

2. 7.305 – 4.12689; nearest whole number

HOMEWORK

Class Periods 1, 4 & 7Page 100, #12 – 24 EVEN PROBLEMS ONLY(12, 14, 16, 18, 20, 22, 24)

Class Periods 2, 3 & 6 (Advanced)Page 100, #12 – 24 EVEN PROBLEMS ONLY(12, 14, 16, 18, 20, 22, 24)

AND #27 & 28