Video: Dividing Decimals up to Three Decimal Places

Calculate 6.126 ÷ 0.327, rounding your answer to the nearest hundredth.

10:31

Video Transcript

Calculate 6.126 divided by 0.327, rounding your answer to the nearest hundredth.

Dividing a decimal by another decimal is a tricky thing to do, especially when each number contains three decimal places. We’d much rather be dealing with whole numbers. With division, if we multiply the dividend and the divisor, or the first and the second number, by the same amount, then the answer to the division will stay the same. Is there a number we could multiply both of these decimals by that would turn them into whole numbers?

Remember that when we multiply by 10, 100, 1000, and so on, the digits shift to the left. All we have to do with the decimals is make the digits shift three places to the left, and then we’ll have some whole numbers. A shift of three places means multiplying by 1000. Let’s see what happens when we multiply both numbers by 1000.

First, we’ll multiply by 10. Notice, how the decimal points stayed where they are but the digits have shifted one place to the left. Let’s multiply by 10 again. This is the same now as if we’d multiplied by 100. And now, to multiply by 1000, we need to shift the digits one more time. Then, we’ll have moved them three places to the left. Look how by multiplying both numbers by 1000, we’ve turned them from decimals into whole numbers. Our division is now 6126 divided by 327. And the great thing is, the answer will be exactly the same as if we divided 6.126 by 0.327.

Now, we can use long division to help find the answer. How many 327s are there in 6126. We’re told that we need to round our answer to the nearest hundredth. Now, to around a number to the nearest hundredth we need to be able to see the thousandths digit too. So, we might need our answer to have three decimal places. We’re still going to keep 6126 as a whole number, but let’s write in our three decimal places to start with. This way, if we need them, we can use them.

Now. We can start dividing. There are no 327s in six or even 61, so we need to consider the first three digits of our number. How many 327s are there in 612? We know there’s definitely one lot of 327. But two lots of 327 would be over 612. So, the number of 327s in 612 is only one. One lot of 327 is only 327, so we can take this away from 612 to find out the remainder.

We can see that some of the digits in the bottom number are larger than those in the top number, so we’re going to have to exchange to help us find the answer. We can start by exchanging 100 for 10 10s. We’ll, now take one of those 10s, so we’re left with 10 10s, and exchange it for 10 ones. Now, we can subtract. 12 take away seven equals five. 10 take away two equals eight. And five take away three equals two. There’s 285 as a remainder.

There aren’t any 327s in 285. So, we need to bring down another digit from the top number. How many 327s are there in 2856? Not sure what your knowledge of the 327 times table is, but we’re going to have to use some facts we know to help us here. The first one we can use is 10 lots of 327, which is 3270. This is too large. Let’s take away one lot of 327 to see what nine times 327 is. We’re going to have to exchange to help us subtract.

10 take away seven equals three. Six take away two equals four. And then, we can just work out 32 take away three equals 29 again. Again, this is too large. Let’s subtract another lot of 327 to find out what eight times 327 is. We can’t take seven ones from three ones, so we’re going to need to exchange again. 13 ones take away seven ones equals six ones. Three 10s take away two 10s equals one 10. Nine 100s take away three 100s leaves us with six 100. And there’s two 1000s in the thousands column.

There are eight lots of 327 in 2856. And as we’ve said, eight lots of 327 is 2616. So, we can subtract this to find out the remainder again. Six take away six is zero. Five take away one equals four. Eight take away six equals two. And the two 1000s in the thousands column cancel each other out. We have a remainder of 240.

Once again, this is too small to divide by 327. Normally, we might say the answer is 18 remainder 240. But we’re told here to round our answer to the nearest hundredth and we need to give our answer as a decimal. So, let’s put a decimal point in at the top as part of our answer and continue bringing down digits until we get an answer that has three decimal places. This is why we wrote point zero zero zero on the end at the start. So, we could bring down the digits if we needed to.

We can see that eight lots of 327 is too large. But we can also see that the answer is going to be seven lots of 327. We just need to calculate what that is. First of all, let’s exchange so that we get to a point where we can subtract each column. 16 ones take away seven ones equals nine ones. 10 10s take away two 10s equals eight 10s. And we could just work out 25 100s take away three 100s equals 22 100s. So, we can definitely say there are seven lots of 327 in 2400.

Seven lots of 327 is 2289. And let’s subtract to find the remainder, again, with exchange a little quicker now. If you need to watch it again, rewind the video to see what’s happening. 10 ones take away nine ones equals one. Nine 10s take away eight 10s equals one 10. Three 100s take away two 100s equals 100. And the two 1000s cancel each other out. We have a remainder of 111. Again, we can’t divide this by 327, so we need to bring down our next digit.

Good job we put the zeros in at the start. How many 327s are there in 1110? We can see that two lots of 327 is going to be 600 and something. So, let’s try to see how close we can get with three lots of 327. And this time, we’ll use short multiplication to find the answer. Seven times three equals 21. Two threes are six, plus the two underneath equals eight. And three threes are nine. This is the closest we’re going to get to 1110. So, there are three 327s in 1110.

We need to subtract once again to find the remainder. There’s been a lot of exchanging we’ve needed to do in these calculations. Now, we’re ready to subtract. 10 ones take away one one equals nine ones. 10 10s take away eight 10s equals two 10s. We can think of the next calculation as 10 100s take away nine 100s. This leaves us with 100. 129 is too small to divide by 327. So, we need to bring down our last digit. And the reason why it’s our last digits, so we’re not going to carry on, is because we only need to give our answer to the nearest hundredth.

At the moment, our answer is 18.73. But we need the thousandth digit just to work out whether to keep it as three or whether to round up the hundredth to four. We know that 327 multiplied by three equals 981. We can estimate that if we add another 327 to this amount, we’ll have four lots of 327, and this should fit into 1290. One add seven equals eight. Eight 10s add two 10s equals 10 10s. Nine 100s plus three 100s plus the one underneath equals 13 100s. This is too large. There are only going to be three lots of 327 in 1290.

At this point, we can stop with the calculation. We know there’ll be a remainder, but it doesn’t matter. Our answer to the nearest hundredth is 18.73. Rather than divide two decimals, we multiplied both of them by 1000 to convert them into whole numbers. But the answer is the same as if we were dividing the decimals. And so, 6.126 divided by 0.327, to the nearest hundredth, is 18.73.

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