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Video: Multiplying Decimals by Integers

Tim Burnham

Calculate 0.043 × 31.

03:32

Video Transcript

Calculate zero point zero four three times thirty-one.

Now when I look at this calculation, I would rather do the calculation forty-three times thirty-one. So in fact, that’s what I’m going to do. Now in order to do that calculation, I’m going to think about what this number actually means.

Well thinking about the place value of each of those digits, I’ve got zero ones or units; I’ve got zero tenths, four hundredths, and three thousandths. So actually I’ve, got forty-three thousandths. And forty-three thousandths can be written like this: forty-three divided by a thousand.

Now that means that my calculation can be rewritten as forty-three thousandths times thirty-one. And one way of doing that calculation is to do forty-three times thirty-one, which is what I said there’s the calculation that I’d rather do, and then take that whole answer and divide by a thousand. So that’s what we’re gonna do.

So let’s write out the calculation in column format like this, forty-three times thirty-one. Now remember that the numbers in this column here are worth ten and the numbers in this column here are only worth ones, so I’ve got three ones and four tens in the first number and one one and three tens in the second number.

Now I’m going to do the multiplication in two parts. First of all, I’m going to do one times forty-three and then I’m gonna do thirty times forty-three. So let’s start with one times forty-three. Well one times three is three, so I can write that digit there. And one times four is four, so I can write that digit there. So one times forty-three is just forty-three.

Now I’m going to do thirty times forty-three. Well thirty times forty-three is just like three times forty-three, only it’s gonna be ten times bigger. So when I multiply my answer by ten, I’m gonna be shifting all the digits one place to the left, which means I’m gonna have a zero in the units column. So now I can do three times forty-three. First of all, three times three is nine, then three times four is twelve.

And to record this number, I’m gonna need a couple of extra columns. So twelve, the two is gonna go in the hundreds column and the one from that is gonna go in the next one along. So that’s the thousands column, so thirty times forty-three is one thousand two hundred and ninety.

Now thirty-one times forty-three is thirty times forty-three plus one times forty-three. So I’m just gonna add these two numbers together: three and zero is three four and nine is thirteen, so that’s gonna be three and then I’m gonna carry one over to the next column. So now I’ve got two, but I’ve got the one that I carried over as well so two and one is three, and then I’ve just got one in the next column. So my final answer is one thousand three hundred and thirty-three.

Well I’ve done this part of the calculation, but I still need to divide that answer by a thousand in order in order to answer the question that they actually asked. And one thousand three hundred and thirty-three divided by a thousand is one point three three three. So the overall answer to the question is one point three three three.