Video: Estimating Differences between Three-Digit Numbers: Rounding

In this video, we will learn how to round to the nearest ten or hundred to estimate the value of differences with numbers up to 1000.

15:27

Video Transcript

Estimating Differences between Three-Digit Numbers by Rounding

In this video, we’re going to learn how to round to the nearest ten or hundred to estimate the value of differences within numbers up to 1000. These two hedgehogs are comparing the number of spines they have. The biggest hedgehog has 428 spines, and the baby hedgehog has 152 spines. To find the difference between these two amounts, we would need to subtract 152 from 428.

A really quick way to find the difference would be to estimate. Both of our numbers are three-digit numbers. This means they both have a hundred, tens, and ones digit, and the digit with the highest value is the hundreds digit. So to help us estimate the difference, we could round both of our numbers to the nearest hundred.

We know that number 428 has four 100s. So we know that this number comes between 400 and the next hundred, which is 500. To help us work out which hundred 428 is nearest to, we need to look to the tens digit. Because our tens digit is less than five, we have to round down to 400. 428 rounded to the nearest hundred is 400.

Now we can round 152 to the nearest hundred. The one digit is worth 100. So we know the number 152 comes between 100 and the next hundred, which is 200. To find out which hundred 152 is nearest to, we have to look to the tens digit. If the tens digit is five or more, we have to round up to 200. As our tens digit is a five, we’re rounding up.

Now that we’ve rounded both of our three-digit numbers to the nearest hundred, we can subtract: 400 take away 200. This is a really easy calculation that we can work out mentally. 400 take away 200 is 200. So we rounded 428 to 400 and we rounded 152 to 200. So we can say the difference between 428 and 152 is about 200.

Let’s practice estimating differences by rounding to the nearest hundred now.

Which number is nearest to 489 subtract 162? Is it 300, 400, or 500?

In this question, we’re asked to find the nearest estimate to 489 take away 162. And each of our three possible answers is a multiple of 100: 300, 400, and 500. So we have to estimate the answer to the nearest hundred. We can do this by rounding both of our three-digit numbers to the nearest hundred.

The number 489 has a four in the hundreds place, worth 400. So we know the number 489 comes after 400 and before the next hundred, which is 500. 489 is between 400 and 500. To find out which hundred our number is nearest to, we need to look to the tens digit. 489 has eight 10s. If this digit is worth five or more, we have to round up. Eight is greater than five, so we need to round up to 500. So we know the nearest hundred to 489 is 500.

Our second three-digit number, 162, has a one in the hundreds place. So 162 comes between 100 and the next hundred, which is 200. To help us decide which hundred 162 is nearest to, we have to look at the tens digit. If the tens digit is worth five or more, we have to round up. And we know that six is greater than five. So we round up to 200. So the nearest hundred to 162 is 200.

Now that we’ve rounded both of our three-digit numbers to the nearest hundred, we can quickly find the difference. 500 take away 200 is 300. The number which is nearest to 489 subtract 162 is 300. We found the difference by rounding both of our three-digit numbers to the nearest hundred.

Another way that we can estimate the difference between two three-digit numbers is to round both numbers to the nearest ten. The tens digit in our first three-digit number is a two, worth two 10s. And we know that two 10s are worth 20. So 428 comes between 420 and 430. But which ten is 428 nearest to?

To round our three-digit number to the nearest ten, we need to look to the ones digit. And we know that when we’re rounding, if this digit is five or more, we have to round up. Eight is worth more than five, so the nearest ten to 428 is 430. We’ve rounded up.

Now we can round our second number to the nearest ten. 152 has five 10s, worth 50. So the ten that comes before 152 is 150. And the ten which comes after is 160. Which ten is 152 nearest to, 150 or 160? To find the nearest ten, we need to look to the ones digit. If this digit is worth five or less, we have to round down. Two is worth less than five, so the nearest ten to 152 is 150.

Now that we’ve rounded both of our three-digit numbers to the nearest ten, we can calculate the difference. We know that zero take away zero is zero. Now we can move into the tens column. We have three 10s, and we need to take away five. We need to regroup. We need to take one of our hundreds and exchange it for 10 10s. Now we can work out 13 10s take away five 10s. And we know that 13 take away five is eight. Now we can just subtract the hundreds. Three 100s take away one 100 leaves us with two 100s. We estimated the difference between our two numbers by rounding each three-digit number to the nearest ten.

Let’s practice what we’ve learned now by answering another question.

Look at this calculation: 715 subtract 326. Estimate the answer by rounding both numbers to the nearest hundred. Estimate the answer by rounding both numbers to the nearest ten. Calculate the exact answer. Tip: Use your estimates to see if your answer is sensible.

In this question, we’re asked to look at the calculation 715 take away 326. We’re subtracting one three-digit number from another. First, we’re asked to estimate the answer by rounding both numbers to the nearest hundred. So let’s start by rounding 715 to the nearest hundred.

We know the number 715 has seven 100s. The hundred which comes before 715 is 700, and the next hundred is 800. So 715 is between 700 and 800. To find the nearest hundred, we need to look to the tens digit, which is a one. And we know that if this digit is less than five, we have to round down. So the nearest hundred to 715 is 700.

Now we need to round 326 to the nearest hundred. The three digit in the number 326 is worth three 100s. So we know the hundred before 326 is 300 and the hundred which comes after 300 is 400. So 326 is between 300 and 400. And just like we did with our first number, we can find the nearest hundred by looking at the tens digit. 326 has two 10s. And we know if the tens digit is less than five, we round down. So the nearest hundred to 326 is 300.

Now that we’ve rounded both of our three-digit numbers to the nearest hundred, we can subtract. 700 subtract 300 is 400.

Next, we need to estimate the answer by rounding both of our numbers to the nearest ten. The number 715 has one 10. So the ten which comes before 715 is 710. And 10 more than 710 is 720. So we know that 715 comes between 710 and 720. Which of these two tens is 715 nearest to? We need to look to the ones digit. 715 has five ones. And we know if this digit is worth five or more, we have to round up. So the nearest ten to 715 is 720.

The number 326 comes between 320 and 330. Again, to find the nearest ten, we need to look at the ones digit, which is a six. Because this digit is worth five or more, again we need to round up. So the nearest ten to 326 is 330.

Now that we’ve rounded both of our three-digit numbers to the nearest ten, we can subtract to find the difference. Let’s start in the ones column. We know that zero take away zero is zero. We’ve got two 10s, and we need to take away three 10s. So we’re going to need to regroup. We need to take 100 and exchange it for 10 10s. Now we’ve got 12 10s, and we need to take away three. And we know that 12 take away three is nine.

Now all we need to do is subtract in the hundreds place. Six 100s take away three 100s leaves us with three 100s. So we rounded both of our three-digit numbers to the nearest ten. And we estimated the difference to be about 390.

Now, for the final part of our question, we have to calculate the exact answer. And we’re given a tip: to use our estimates to see if our answer is sensible. We’ve already estimated the answer by rounding to the nearest hundred and the nearest ten. Let’s calculate 715 take away 326.

We have five ones, and we need to take away six. We’re going to need to regroup. We need to take one 10 and exchange it for 10 ones. Now we can subtract our six ones from 15. We know that 15 take away six is nine. Now we can subtract in the tens column. We’re going to need to regroup again. We have no tens, and we need to take away two. So we can exchange one of our hundreds for 10 10s. 10 10s take away two 10s leaves us eight 10s.

Finally, we just need to subtract in the hundreds column. Six 100s take away three 100s leaves us with three 100s. 715 subtract 326 is 389. This is close to our estimate of 400. And when we rounded both numbers to the nearest ten, our estimate was 390. 389 is very close to 390.

We estimated 715 subtract 326 by rounding both numbers to the nearest hundred, which gave us 400. When we rounded both numbers to the nearest ten, our estimate was 390. And we worked out the exact answer by subtracting 326 from 715. Our exact answer was 389.

What have we learned in this video? We have learned that we can estimate differences by rounding to the nearest ten or the nearest hundred. We’ve also learned that we can use estimates to check our answers.

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