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All courses Math Foundations · MF.NS.2 2 of 60
Estimate sums, products, quotients, and percent results, then judge whether an exact answer is reasonable.

Estimate a sum with rounding

Problem
Estimate the sum of 48.6 and 31.2 by rounding each number to the nearest whole number and then adding the rounded numbers.
Your answer

Hint

Look at the tenths digit of each addend. In 48.6 the tenths digit is 6, and in 31.2 it is 2.

To round to the nearest whole number, a tenths digit from 5 through 9 increases the whole number by 1. A tenths digit from 0 through 4 keeps the whole number unchanged. Round both addends before adding.

Solution walkthrough

01

Use the tenths digits

\[6~\ge~5,\;~2~<~5\]

The tenths digit decides nearest-whole rounding. The 6 in 48.6 means round up. The 2 in 31.2 means keep the whole-number part.

02

Round both addends

\[48.6~\to~49;\quad~31.2~\to~31\]

Increase 48 to 49 because its tenths digit is at least 5. Keep 31 because its tenths digit is below 5. Both decimals have now been replaced by whole numbers.

03

Add the rounded numbers

\[49~+~31~=~80\]

Add 31 in two small parts: 49 + 30 = 79, and then 79 + 1 = 80. So the estimated sum is 80.

04

Check the estimate

\[48.6~+~31.2~=~79.8;\quad~80~-~79.8~=~0.2\]

The exact sum is 79.8. It is only 0.2 below the estimate 80, so the rounded result is reasonable.

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Another way

  1. Think about the rounding changes: 48.6 increases by 0.4 to 49, while 31.2 decreases by 0.2 to 31. The estimate is therefore 0.2 above the exact sum 79.8, which gives 80.

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Common mistake

Do not round one addend and leave the other one exact. The requested method rounds both 48.6 and 31.2 to whole numbers first, then adds 49 + 31.