Video: Estimating the Sum of Two Three-Digit Numbers

Look at this calculation. 572 + 241 = _. Estimate the answer by rounding both numbers to the nearest hundred. Estimate the answer by rounding both numbers to the nearest ten. Find the exact answer.

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Video Transcript

Look at this calculation, 572 plus 241. Estimate the answer by rounding both numbers to the nearest hundred. Then, estimate the answer by rounding both numbers to the nearest ten. And then, find the exact answer.

In this problem, we have three things to do. We are asked to estimate the answer in two different ways. And then, we’re also asked to find the exact answer. Let’s start by estimating the answer by rounding both numbers to the nearest hundred. 572 is in between two multiples of a hundred, 500 and 600. The halfway point is 550. And 572 is more than this. So, the nearest hundred is 600.

Let’s round our second number. 241 is in between 200 and 300. But which one is it closest to? Well, 241 is less than the halfway point which is 250. So, we could draw it about here on our number line. So, we can see that the nearest hundred is 200. And so, by rounding both numbers to the nearest hundred, our calculation becomes 600 plus 200, which is a lot quicker to workout than 572 add 241.

600 plus 200 equals 800. It’s not the exact answer to our calculation, but it’s a good estimate. When we round both numbers to the nearest hundred, the answer is 800. What sort of estimate will we get if we round both numbers to the nearest ten? Let’s find out.

The two multiples of ten either side of 572 are 570 and 580. Which one is it closest to? 572 is nearest to 570. So, let’s write that as our first number in our addition. What is 241 rounded to the nearest ten? Well, 241 comes between 240 and 250. And again, we need to round it down. To the nearest ten, 241 is 240. And so, our addition has become 570 plus 240.

Let’s calculate the estimation now by adding these two numbers together. Zero ones plus zero ones equals zero ones. Seven 10s plus four 10s equals 11 10s. So, we take 10 of those 10s and we exchange them for 100. And then, we add the hundreds. 500 plus 200 equals 700, and remember, the 100 that we exchanged, 800. And so, by rounding both numbers to the nearest 10, we get an answer of 810.

Finally, we’re asked to find the exact answer. Let’s see how accurate our estimations are. And let’s see whether we get a sensible answer. A good tip is to use our estimates to see if our answer is sensible. If we got an answer of 325, we might think that we’ve worked it out incorrectly because our two estimates are around 800. So, we’d expect our answer to be about 800. Let’s see whether we’re correct.

Two ones plus one one equals three ones. Seven 10s plus four 10s, we’ve already done this, equals 11 10s. And if you remember, we had to exchange 10 of those 10s for 100. And then, add the hundreds. 500 plus 200 equals 700. And remember, we’ve exchanged 100 as well. That makes 800 in total.

So, the exact answer to our calculation is 813. First, we rounded both numbers to the nearest hundred, and we got an estimate of 800. Next, we rounded both numbers to the nearest 10, and we got another estimation. This time of 810. And finally, we worked out the exact answer. And this showed us our estimations were quite accurate. The exact answer is 813.

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