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 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

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

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

Insert Lesson Title Here Course 1 3-2 Estimating Decimals Insert Lesson Title Here Vocabulary clustering front-end estimation

Course 1 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.

Additional Example 1: Health Application Course 1 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) 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

3-2 Estimating Decimals Try This: Example 1 Course 1 3-2 Estimating Decimals Try This: Example 1 Abner wants to run, roller blade, and snow ski for 60 minutes each. About how many calories will he burn in all? (Running = 185.5 calories, roller blading = 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

3-2 Estimating Decimals Remember! Course 1 3-2 Estimating Decimals When rounding, 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. Remember!

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. The sum is about 12. 7 + 5 = 12 Round to the tenths. 9.705 9.7 Align. – 0.2683 –0.3 Subtract. 9.4

3-2 Estimating Decimals Try This: Example 2 Course 1 3-2 Estimating Decimals Try This: 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

3-2 Estimating Decimals Remember! Course 1 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!

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 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.

3-2 Estimating Decimals Try This: Example 3 Course 1 3-2 Estimating Decimals Try This: 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.

Course 1 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.

Additional Example 4: Using Front-End Estimation 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. 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 Course 1 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 to 0, 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.

3-2 Estimating Decimals Try This: Example 4 Course 1 3-2 Estimating Decimals Try This: 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.

3-2 Estimating Decimals Try This: Example 4 Course 1 3-2 Estimating Decimals Try This: Example 4 You can estimate a range for the sum by adjusting the decimal part of the numbers. Round the decimals to 0, 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.

Insert Lesson Title Here Course 1 3-2 Estimating Decimals Insert Lesson Title Here Lesson Quiz: Part 1 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

Insert Lesson Title Here Course 1 3-2 Estimating Decimals Insert Lesson Title Here Lesson Quiz: Part 2 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