Chapter 3, Section 2, Page 98 “Estimating Decimals”

Warm Up Order the decimals from least to greatest , 18.7, , 9.66, 9.6, Write each in words , 18.7, , 9.076, 9.6, 9.66 three and seventy-two thousandths six and one thousand two hundred fifty-eight ten-thousandths

MA.6.A.5.2 Estimate the results of computations with…decimals…and judge the reasonableness of the results. Sunshine State Standards

When numbers are about the same value, you can use clustering to estimate. Clustering means rounding the numbers to the same value. Vocabulary You Need to Know Compatible numbers are close to the numbers that are in the problem and are helpful when you are solving the problem mentally.

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 = calories, ice skating = calories, and water skiing = calories) The addends cluster around To estimate the total number of calories, round each addend to 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 = calories, roller skating = calories, and snow skiing = calories) The addends cluster around To estimate the total number of calories, round each addend to 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! 5 or more, raise the score! 4 or less, let it rest!

Rounding Decimals to Estimate Sums and Differences Estimate by rounding to the indicated place value. A ; ones B – ; tenths Round to the nearest whole number = 12 The sum is about Round to the tenths.Align. 9.4 Subtract. – –0.3

Example 2 Estimate by rounding to the indicated place value. A ; ones B – ; tenths Round to the nearest whole number = 10 The sum is about Round to the tenths.Align. 8.4 Subtract. – –0.5

Using Compatible Numbers to Estimate Products and Quotients Estimate each product or quotient. A  1.98 B ÷  2 = and 2 are compatible. 75 ÷ 25 = 3 75 and 25 are compatible. So, ÷ is about 3. So  1.98 is about 70.

Example 3 Estimate each product or quotient. A  4.98 B ÷  5 = and 5 are compatible. 60 ÷ 20 = 3 60 and 20 are compatible. So, ÷ is about 3. So  4.98 is about 100.

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.

Using Front-End Estimation Estimate a range for the sum Use front-end estimation Add the whole numbers only The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate at least 48 The exact answer of is greater than 48.

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 Add the adjusted decimal part of the numbers Add the whole-number estimate and this sum = The adjusted decimals are greater than the actual decimal, so is an overestimate. The estimated range for the sum is from to

Example Estimate a range for the sum Use front-end estimation Add the whole numbers only The whole-number values of the decimals are less than the actual numbers, so the answer is an underestimate at least 58 The exact answer of is greater than 58.

Lesson Quiz Estimate each product or quotient cm  ÷ The snowfall in December, January, and February was cm, cm, and cm, respectively. About how many total centimeters of snow fell during the three months? Estimate by rounding to the indicated place value ; tenths – ; nearest whole number

HOMEWORK Class Periods 1, 4 & 7 Page 100, #12 – 24 EVEN PROBLEMS ONLY (12, 14, 16, 18, 20, 22, 24) Class Periods 2, 3 & 6 (Advanced) Page 100, #12 – 24 EVEN PROBLEMS ONLY (12, 14, 16, 18, 20, 22, 24) AND #27 & 28