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3-2 Estimating Decimals Learn to estimate decimal sums, differences, products, and quotients.

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3-2 Estimating Decimals Vocabulary clustering front-end estimation

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3-2 Estimating Decimals When numbers are about the same value, you can use clustering to estimate. Clustering means rounding the numbers to the same value.

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3-2 Estimating Decimals 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) 165.5170 The addends cluster around 170. 177.5170 To estimate the total number of calories, round each addend to 170. 171.5+ 170 Add. 510 Nancy burns about 510 calories.

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3-2 Estimating Decimals 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) 185.5190 The addends cluster around 190. 189.5190 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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3-2 Estimating Decimals 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!

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3-2 Estimating Decimals 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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3-2 Estimating Decimals Check It Out: 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

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3-2 Estimating Decimals Compatible numbers are close to the numbers that are in the problem and are helpful when you are solving the problem mentally.Remember!

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3-2 Estimating Decimals 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.

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3-2 Estimating Decimals Check It Out: 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.

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3-2 Estimating Decimals 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.

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3-2 Estimating Decimals 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. 36.9736 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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3-2 Estimating Decimals 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. 0.861.00 Add the decimal part of the numbers. 0.971.00 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.

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3-2 Estimating Decimals Check It Out: Example 4 Estimate a range for the sum. 8.92 + 47.88 + 3.41 Use front-end estimation. 8.92 8 Add the whole numbers only. 47.8847 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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3-2 Estimating Decimals Check It Out: Example 4 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. 0.921.00 Add the decimal part of the numbers. 0.881.00 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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