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!
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.
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!
Here is a summary showing how to estimate a sum
