Estimating a Sum

Estimating a sum by rounding to get the best estimate is the goal of this lesson. Notice that we try to estimate. We don't need to have an exact answer!
Estimating a sum by rounding

Notice that for numbers with two digits, there can only be one estimate because you can only round to the tens place.

Estimate the following sums: 36 + 21, 74 + 15, and 85 + 24

36 + 21 = 40 + 20 = 60

74 + 15 = 70 + 20 = 90

85 + 24 = 90 + 20 = 110

For numbers with three digits, you can get two estimates.

Estimate the following sums: 176 + 432, 250 + 845, and 986 + 220.

Rounding 176 and 432 to the nearest hundred, gives 200 + 400 = 600.

However, rounding 176 and 432 to the nearest ten, gives 180 + 430 = 610.

The exact answer is 176 + 432 = 608. Notice that 610 is closer to 608 than 600, so rounding to the nearest 10 gives a better estimate.  

Rounding 250 and 845 to the nearest hundred gives 300 + 800 = 1100.

However, rounding 250 and 845 to the nearest ten gives 250 + 850 = 1100.

Notice this time, however, that you get the same answer for the estimate. Therefore, either rounding to the nearest 100 or to the nearest 10 will yield a good estimate.

The exact answer is 250 + 845 = 1095.

Rounding 986 and 220 to the nearest hundred gives 1000 + 200 = 1200.

However, rounding 986 and 220 to the nearest ten gives 990 + 220 = 1210.

The exact answer is 986 + 220 = 1206

This shows that rounding to the nearest ten gives a better approximation.

However, notice that if you were trying to estimate 985 + 220, everything else will stay the same, but the exact answer will be 1205.

1205 is neither closer to 1200 nor to 1210

Still, if you were trying to estimate 984 + 220, the exact answer will be 1204.

Since 1204 is closer to 1200 than 1210, this time rounding to the nearest hundred gives a better estimate.

Important things to keep in mind: When rounding numbers with at least 3 digits, rounding to a lower place does not always yield a better estimate. When estimating sums, it really depends on the problems!

Estimating a sum quiz. See how well you can it with the quiz below.

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