3-2 estimating decimals homework presentation homework presentation

3-2 Estimating Decimals

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


Vocabulary

clusteringfront-end estimation


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


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 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!


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




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


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

Remember!Remember!


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

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.




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.


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.


Additional 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 decimal part of the numbers.

0.97 1.00 Add the whole-number estimate and the adjusted estimate. 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.



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.



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.



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?


1. 3.07442 + 1.352; tenths

2. 7.305 – 4.12689; nearest whole number

Check For Understanding

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