3-2 Estimating Decimals Warm Up Problem of the Day Lesson Presentation Course 1 Warm Up Problem of the Day Lesson Presentation

three and seventy-two thousandths 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

Calculate your age in months. Problem of the Day Calculate your age in months. Possible answer: 11 yr 8 mo = 140 mo

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

Vocabulary clustering front-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) The addends cluster around 170. 165.5 170 To estimate the total number of calories, round each addend to 170. 177.5 170 171.5 + 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) The addends cluster around 190. 185.5 190 To estimate the total number of calories, round each addend to 190. 189.5 190 191.5 + 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!

Estimate by rounding to the indicated place value. 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. The sum is about 12. 7 + 5 = 12 Round to the tenths. 9.705 9.7 Align. – 0.2683 –0.3 Subtract. 9.4

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. The sum is about 10. 6 + 4 = 10 Round to the tenths. 8.898 8.9 Align. –0.4619 –0.5 Subtract. 8.4

Compatible numbers are close to the numbers that are in the problem and are helpful when you are solving the problem mentally. 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 and 2 are compatible. 35  2 = 70 So 33.83  1.98 is about 70. 75 ÷ 25 = 3 75 and 25 are compatible. So, 72.77 ÷ 26.14 is about 3.

Check It Out: Example 3 Estimate each product or quotient. A. 22.12  4.98 B. 62.31 ÷ 18.52 20 and 5 are compatible. 20  5 = 100 So 22.12  4.98 is about 100. 60 ÷ 20 = 3 60 and 20 are compatible. So, 62.31 ÷ 18.52 is about 3.

You can also use front-end estimation to estimate with 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.

Additional Example 4: Using Front-End Estimation Estimate a range for the sum. 7.86 + 36.97 + 5.40 Use front-end estimation. Add the whole numbers only. 7.86 7 The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate. 36.97 36 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. Add the decimal part of the numbers. 0.86 1.00 Add the whole-number estimate and the adjusted estimate. 0.97 1.00 0.40 + 0.50 The adjusted decimals are greater than the actual decimal, so 50.50 is an overestimate. 2.50 48.00 + 2.50 = 50.50 The estimated range for the sum is from 48.00 to 50.50.

Check It Out: Example 4 Estimate a range for the sum. 8.92 + 47.88 + 3.41 Use front-end estimation. Add the whole numbers only. 8.92 8 The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate. 47.88 47 3.41 + 3 at least 58 The exact answer of 8.92 + 47.88 + 3.41 is 58 or greater.

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. Add the decimal part of the numbers. 0.92 1.00 Add the whole-number estimate and the adjusted estimate. 0.88 1.00 0.41 +0.50 The adjusted decimals are greater than the actual decimal, so 60.50 is an overestimate. 2.50 58.00 + 2.50 = 60.50 The estimated range for the sum is from 58.00 to 60.50.

Lesson Quiz 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 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