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

2. Course 1 3-2 Estimating Decimals 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

3. Course 1 3-2 Estimating Decimals Problem of the Day Calculate your age in months. Possible answer: 11 yr 8 mo = 140 mo

4. Course 1 3-2 Estimating Decimals Learn to estimate decimal sums, differences, products, and quotients.

5. Course 1 3-2 Estimating Decimals Vocabulary clustering front-end estimation

6. Course 1 3-2 Estimating Decimals Clustering means rounding the numbers to the same value.

7. Course 1 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.

8. Course 1 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!

9. Course 1 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

10. Course 1 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

11. Course 1 3-2 Estimating Decimals Compatible numbers in math means it can go into it evenly. Use for division.Remember!

12. Course 1 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 75 ÷ 25 = 3 75 and 25 are compatible. So, 72.77 ÷ 26.14 is about 3.

13. Course 1 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 Or 22 x 5 60 ÷ 20 = 3 60 and 20 are compatible. So, 62.31 ÷ 18.52 is about 3.

14. Course 1 3-2 Estimating Decimals Front-end estimation means to use only the whole-number part of the decimal.

15. Course 1 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.

16. Course 1 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.

17. Course 1 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.

18. Course 1 3-2 Estimating Decimals Lesson Quiz Estimate each product or quotient. 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? Estimate by rounding to the indicated place value. 3 4.5 1. 3.07442 + 1.352; tenths 2. 7.305 – 4.12689; nearest whole number