course 1 3-2 estimating decimals 3-2 estimating decimals course 1 warm up warm up lesson...

Course 1

3-2 Estimating Decimals3-2 Estimating Decimals

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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3-2 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

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Problem of the Day

Calculate your age in months.

Possible answer: 11 yr 8 mo = 140 mo

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Learn to estimate decimal sums, differences, products, and quotients.

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Vocabulary

clusteringfront-end estimation

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Clustering means rounding the numbers to the same value.

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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.

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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!

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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 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

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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

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Compatible numbers in math means it can go into it evenly. Use for division.

Remember!Remember!

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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

75 ÷ 25 = 3 75 and 25 are compatible.

So, 72.77 ÷ 26.14 is about 3.

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A. 22.12 4.98

B. 62.31 ÷ 18.52

20 5 = 100 Or 22 x 5

60 ÷ 20 = 3 60 and 20 are compatible.

So, 62.31 ÷ 18.52 is about 3.

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Front-end estimation means to use only the whole-number part of the decimal.

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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 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 48 or greater.

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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 58 or greater.

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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.

0.92 1.00Add the decimal part of the numbers.

0.88 1.00 Add the whole-number estimate and the adjusted estimate. 0.41 +0.50

2.50

58.00 + 2.50 = 60.50

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

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

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Lesson Quiz


3

14

80

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?


3

4.51. 3.07442 + 1.352; tenths

2. 7.305 – 4.12689; nearest whole number

course 1 3-2 estimating decimals 3-2 estimating decimals course 1 warm up warm up lesson...

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