# 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!

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

For example, 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

For example, 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

Moreover, rounding 250 and 845 to the tens gives 250 + 850 = 1100

The exact answer is 250 + 845 = 1095. Notice this time, However, that you get the same answer.

So, either way will yield a good estimate.

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 approxiamation

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.

Moral of the story: When rounding numbers with at least 3 digits, rounding to a lower place does not always yield a better estimate.

Therefore, when estimating sums, it really depends on the problems!

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