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

3-2 Estimating Decimals Vocabulary clustering front-end estimation

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.

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 = 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.

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 = 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.

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!

3-2 Estimating Decimals Additional Example 2: 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

3-2 Estimating Decimals Check It Out: 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

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!

3-2 Estimating Decimals Additional Example 3: 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.

3-2 Estimating Decimals Check It Out: 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.

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.

3-2 Estimating Decimals Additional Example 4: 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 48 or greater.

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

3-2 Estimating Decimals Check It Out: Example 4 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 58 or greater.

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