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Estimating Decimals

Course 1

Warm Up

Order 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

Estimating Decimals

Course 1

Problem of the Day

Calculate your age in months.

Possible answer: 11 yr 8 mo = 140 mo

Estimating Decimals

Course 1

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

Estimating Decimals

The addends cluster around 170.

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

Add.

Course 1

Additional 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

177.5

170

171.5

+ 170

510

Nancy burns about 510 calories

Estimating Decimals

The addends cluster around 190.

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

Add.

Course 1

Try This: Example 1

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

185.5

190

189.5

190

191.5

+ 190

570

Abner burns about 570 calories

Estimating Decimals

Remember!

- When rounding, 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.

Course 1

Estimating Decimals

– 0.2683 –0.3

Round to the nearest whole number.

The sum is about 12.

Round to the tenths.

Align.

Subtract.

Course 1

Additional Example 2: 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

7 + 5 = 12

9.705 9.7

9.4

Estimating Decimals

–0.4619 –0.5

Round to the nearest whole number.

The sum is about 10.

Round to the tenths.

Align.

Subtract.

Course 1

Try This: 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

6 + 4 = 10

8.898 8.9

8.4

Estimating Decimals

Remember!

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

Course 1

Estimating Decimals

35 and 2 are compatible.

75 and 25 are compatible.

Course 1

Additional Example 3: Using Compatible Numbers to Estimate Products and Quotients

Estimate each product or quotient.

A. 33.83 1.98

B. 72.77 ÷ 26.14

352 = 70

So 33.83 1.98 is about 70.

75 ÷ 25 = 3

So, 72.77 ÷ 26.14 is about 3.

Estimating Decimals

20 and 5 are compatible.

60 and 20 are compatible.

Course 1

Try This: Example 3

Estimate each product or quotient.

A. 22.12 4.98

B. 62.31 ÷ 18.52

205 = 100

So 22.12 4.98 is about 100.

60 ÷ 20 = 3

So, 62.31 ÷ 18.52 is about 3.

Estimating Decimals

Course 1

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.

Estimating Decimals

Add the whole numbers only.

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

Course 1

Additional Example 4: Using Front-End Estimation

Estimate a range for the sum.

7.86 + 36.97 + 5.40

Use front-end estimation.

7.86

7

36.97

36

5.40

+ 5

at least 48

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

Estimating Decimals

Add the decimal part of the numbers.

Add the whole-number estimate and the adjusted estimate.

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

Course 1

Additional Example 4 Continued

You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals to 0, 0.5, or 1.

0.86

1.00

0.97

1.00

+ 0.50

0.40

2.50

48.00 + 2.50 = 50.50

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

Estimating Decimals

Add the whole numbers only.

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

Course 1

Try This: Example 4

Estimate a range for the sum.

8.92 + 47.88 + 3.41

Use front-end estimation.

8.92

8

47.88

47

3.41

+ 3

at least 58

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

Estimating Decimals

Add the decimal part of the numbers.

Add the whole-number estimate and the adjusted estimate.

The adjusted decimals are greater than the actual decimal, so 60.50 is an overestimate.

Course 1

Try This: Example 4

You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals to 0, 0.5, or 1.

0.92

1.00

0.88

1.00

0.41

+0.50

2.50

58.00 + 2.50 = 60.50

The estimated range for the sum is from 58.00 to 60.50.

Estimating Decimals

Course 1

Insert Lesson Title Here

Lesson Quiz: Part 1

Estimate by rounding to the indicated place value.

1. 3.07442 + 1.352; tenths

2. 7.305 – 4.12689; nearest whole number

4.5

3

Estimating Decimals

Course 1

Insert Lesson Title Here

Lesson Quiz: Part 2

Estimate each product or quotient.

3. 6.75 1.82

14

4. 10.5 ÷ 3.42

3

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?

80

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