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

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

4. 3-2 Estimating Decimals Vocabulary clustering front-end estimation

5. 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.

6. 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.

7. 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.) 190 × 3 = 570 calories

8. 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. 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. 3-2 Estimating Decimals Check It Out: Example 2 Estimate by rounding to the indicated place value. 6.09 + 3.72; ones 6 + 4 = 10

11. 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!

12. 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.

13. 3-2 Estimating Decimals Check It Out: Example 3 Estimate each product or quotient. 62.31 ÷ 18.52 60 ÷ 20 = 3

14. 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.

15. 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 greater than 48.

16. 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 adjusted decimal part of the numbers. 0.971.00 Add the whole-number estimate and this sum. 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.

17. 3-2 Estimating Decimals Check It Out: Example 4 Estimate a range for the sum. 8.92 + 47.88 + 3.41 underestimate: 8 + 47 + 3 = 58 overestimate: 9 + 48 + 3.5 = 60.5 from 58.00 to 60.50

18. 3-2 Estimating Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

19. 3-2 Estimating Decimals Lesson Quiz Estimate each product or quotient. 3 14 80 cm 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

20. 3-2 Estimating Decimals 1. Estimate by rounding to the indicated place value. 5.891+9.326; hundredths A. 14.21 B. 14.22 C. 15.21 D. 15.22 Lesson Quiz for Student Response Systems

21. 3-2 Estimating Decimals 2. Estimate by rounding to the indicated place value. 29.35-17.92; nearest whole number A. 10 B. 11 C. 12 D. 13 Lesson Quiz for Student Response Systems

22. 3-2 Estimating Decimals 3. Identify the estimate of the product of 16.77  3.81. A. 48 B. 51 C. 64 D. 68 Lesson Quiz for Student Response Systems

23. 3-2 Estimating Decimals 4. Identify the estimate of the quotient of 17.43  3.91. A. 6 B. 5 C. 4 D. 3 Lesson Quiz for Student Response Systems

24. 3-2 Estimating Decimals 5. The weight of three students in a class are 48.23 pounds, 54.81 pounds, and 45.3 pounds. Identify the total weight of the students. A. 130 lb B. 140 lb C. 150 lb D. 160 lb Lesson Quiz for Student Response Systems