Video: Multiplying a Decimal by Another

Calculate 0.71 × 0.53.

02:29

Video Transcript

Calculate 0.71 times 0.53.

To multiply decimals, first we should ignore the decimal points and the zeros in front of them. We will come back to them later. Let’s first multiply 71 and 53.

To begin, we look at the ones place. So we have one and three, and one times three is three. And again, we found that by multiplying one and three. Now we also need to take three and multiply it to the seven, and three times seven is 21.

So now we need to look at the five. And we will take five times one, because of course that’s what we started with the three, and that’s what we will always do. So five times one is five. However, that five really stands for 53, right? So if the five really stands for a 50, we need to put a zero here for a place value holder.

So five times one is five, and now five times seven is 35. And our next step is to add. So in the ones, we have three plus zero, which is three, and then one plus five, which is six, five plus two, which is seven. And then we have a three. So we have 3763.

Now if we’re multiplying decimals together, it doesn’t make sense to have such a big number. Well, the reason why is we need to take care of the decimal point, where should it go. To place the decimal point, we must count the number of decimal places in the factors.

The number of decimal places in the product is equal to that sum. The sum of the decimal places in these factors is four, and here’s why. We have 0.71 and 0.53. Here’s one, two, three, four. So there are four decimal places. That’s their sum. So we must place the decimal point in the product four places from the right.

So here’s all the way to the right with a decimal point, and we need to place it four places from the right. So we’ll need to go to the left: one, two, three, and four. So here’s our decimal point. And since there’s no number in front, it’s a good idea to put a zero there. This makes the decimal point stick out. So our final answer will be 0.3763.

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