Video: Multiplying a Decimal by a Two-Digit Integer

Calculate 3.788 × 98.

07:53

Video Transcript

Calculate 3.788 multiplied by 98.

Now there’re several ways we could answer this question. For example, we could multiply 3.788 by 100 and then take away two lots of 3.788. But it would be a lot easier if we were working with whole numbers. The calculation would be a lot less tricky if we were trying to find 3788 multiplied by 98. But we can do that as long as we remember to put the decimal point in the correct place at the end. Here’s what our calculation should look like, 3.788 multiplied by 98. So what we can do to start with is to erase the decimal point. This isn’t just a trick. What we’ve done by rubbing out the decimal point is really shift the digits.

Here’s the number 3.788. And if we shift the digits three places to the left, we get 3788. And it’s as if we’ve rubbed out the decimal point. Now shifting digits three places to the left is the same as multiplying by 1000. So although we just said rub out the decimal point, what we really mean is multiply the first number by 1000. This then makes the calculation easier to work out. But we need to remember at the end, we’re going to have to divide by 1000 to put our answer exactly as it should be.

First of all then, let’s multiply 3788 by the eight digit in 98. Eight ones multiplied by eight equals 64 ones. So we’re gonna write the four in the ones place and exchange our 60 ones for six tens. A similar calculation in the next column. Eight tens multiplied by eight is 64 tens. We’ve got six tens already underneath. So this takes us to 70 tens, which are the same as seven hundreds. Seven hundreds multiplied by eight equals 56 hundreds. We’ve also got seven hundreds underneath. So this takes us to 63 hundreds or 6300. And finally, three thousands multiplied by eight equals 24 thousands plus the six underneath 30000. So 3788 multiplied by eight equals 30304. Let’s cross out the numbers that we’ve exchanged just so that we don’t add them later.

Now we need to multiply 3788 by the nine digit in 98, which of course represents 90. Now 90 is a multiple of 10. So multiplying by 90 is the same as multiplying by 10 and then by nine. When we multiply any number by 10, the digits shift one place to the left. So that’s easy enough to do. If we write a zero in the ones place, then all our answer as we fill it in is going to be shifted one place to the left. Our answer will become 10 times larger. So we’ve done the multiply-by-10 part of multiplying by 90. Now, we just need to multiply by nine.

It makes it a lot easier to think of it like this. If we’re working out eight times 10, it would be worth 80. So eight times nine is one less eight than 80. It’s 72. So we’ll write the two. And we’ll exchange the seven. We have the same digit in the next column. We know eight times nine is 72. But we’ve now exchanged seven underneath. So this will be 79 this time. We know seven 10s or 10 sevens would be 70. So seven nines or nine sevens will be seven less than 70. That’s 63. But we’ve got seven underneath. So that takes us back up to seven 10s. And it’s 70. We’ve got a lot of exchanging of sevens going on here. And finally, three nines are 27, nine, 18, 27. We’ve got seven underneath that we need to include. 27 add seven equals 34, 340920.

Now we need to add these two parts together to find the overall total. And once again, we’ll cross through the digits so that we don’t include them when we add. Four ones plus zero ones equal four ones. Zero tens plus two tens equals two tens. Then we’ve got three hundreds plus nine hundreds, which equals 12 hundreds. The same as two hundreds and one lot of 10 hundreds or 1000. So we’ll exchange that underneath the thousands place. There aren’t any thousands to add a part from the one that we’ve just exchanged. We’ll plug that in. Three ten thousands plus four ten thousands equals seven lots of ten thousands. And the number of hundred thousands is three. The answer to our multiplication is 371224.

But remember, we haven’t solved the problem. We weren’t asked to multiply 3788 by 98. We needed to calculate 3.788 multiplied by 98. If you remember at the start, we made the calculation easier by erasing the decimal point. But we said what we were really doing was multiplying the number by 1000. Now what we can do is to put the decimal point back in. We’ll put it back into the number at the start. And we can put it back in aligned with this number at the start, all the way through our calculation.

Now, this may seem like we’re just in a very clever trick. All we’ve done is rub out a point and then put it back in at the end. But we know the maths behind what we’ve done. We multiplied our first number by 1000. And this shifted the digits three places to the left. If you remember, this gave us the answer 371224. But we did say when we finally answered the question, we were going to have to put it right and divide by 1000. Dividing by 1000 shifts digits three places in the opposite direction as multiplying. So it shifts them to the right. So watch how our number changes as we shift the digits three places to the right. One, two, three. Look how dividing by 1000 is exactly the same as putting the decimal point back where it belonged.

We turned the number in our calculation into whole numbers to help us work out the answer. We then used column multiplication to find the answer. And then at the end, we divided by 1000 again to convert our whole number back into a decimal and find the correct answer.

3.788 multiplied by 98 equals 371.224.

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