Multiplying decimals word problems | Decimal multiplication | Grade 5 (TX TEKS) | Khan Academy

We are told James' dog weighs 2.6 kg, and How's dog weighs 3.4 times as much as James' dog. How much does How's dog weigh? Pause this video and try to figure that out.

Well, How's dog is 3.4 times the weight of James's dog, which is 2.6. So we just have to multiply 3.4 * 2.6.

Before we do that, let's just think about what should this roughly be. So this is between three and four, and this is between two and three. If I had two times three, if I took the lower end for both of them, that would get you around six. And if I took 3 * 4, that would be around 12.

So this should be someplace between 6 and 12. Now let's just think about this without decimals. So let's just imagine 345 (so the same digits but without the decimals) times 26. What would this be? Because our answer is actually going to have the same digits in it, but we just have to figure out where to put the decimal, and hopefully that estimation we just did will help us.

So 5 * 6 is 30, 4 * 6 is 24 + 3 is 27. 3 * 6 is 18 + 2 is 20. Now let's go to the tens place, so I'll put a zero there because I'm dealing with the tens. 2 * 5, and let me cross these out; don’t need these anymore.

2 * 5 is 10; regroup that one. 2 * 4 is 8 + 1 is 9. 2 * 3 is 6. Now let me add up all of this business. I get 0, 7, 9, 8. So if this has the same digits: 8, 9, 70, where do we think we're going to put the decimal?

If it was 2 * 3, we'd get to six. If it was 3 * 4, we'd get to 12. So the only place to put the decimal here that would be in between 6 and 12 would be right over there. But why does that make sense?

Well, one way to think about it is to go from 3.4 to 345. We would have to multiply by 100; we'd have to move this decimal over to the right twice every time you're multiplying by 10. To go from 2.6 to 26, we'd have to multiply by 10; we'd have to multiply this decimal over to the right once.

So if you're multiplying by 100 and by 10, this thing right over here is going to be 100 times 10 larger than this thing, or this is going to be a thousand times larger than this. So if you want to figure out what this is going to be, you just need to divide by a thousand.

So you divide by 10, by 100, by a thousand, you get the decimal right over there. But the most important thing is does this make sense? That a number a little over three times a number a little over two, that should be between 6 and 12. It shouldn't be 89 or 897 or 8 or 8,970.

Let's do another example: Ben rides his electric scooter for 1.2 hours at a speed of 9.3 km per hour. How many kilometers does he ride in total? Pause this video and see if you can figure that out.

So once again, we're just going to multiply these decimals. We're going to have 1.2 * 9.3. We could do the same idea; let's just think about it without the decimals first: 12 and 93.

It is good to think about this. To go from 1.2 to 12, you have to multiply by 10, and to go from 9.3 to 93, you also have to multiply by 10. So once I take this product, whatever the answer is going to be, is going to be, we're multiplying both of these numbers by 10 and then multiplying them together.

So whatever product I get is going to be 100 times bigger than whatever answer should be over here. To go back, we could divide by 100. Another way to think about it is we can estimate this is 1.2 * 9.3, so a little bit more than 1 * a little bit more than 9.

So I don't know; that feels like that should be maybe 10 or 11. It shouldn't be in the hundreds, or it shouldn't be in the thousands, or it shouldn't be less than one. It should be around 10 or 11 or 12 or something like that, so that's also a good check to make sure we're putting the decimal in the right place.

But let's just work through this: 3 * 2 is 6, 3 * 1 is 3. This is turning into a bit of a song. Now we go to the tens place: 9 * 2 is 18, and then 9 * 1 is 9 + 1 is 10.

I'm going to add all of that together, and I'm going to get: 6 plus 0 is 6, 3 + 8 is 11, regroup the one, 1 plus 0 is one, and then we just bring this one down.

So the digits are going to be 1, 1, 1, 6. Where do we put the decimal? Well, we reason that this is going to be a little bit more than 9.3; maybe it'll be 10 or 11.

The only place to put the decimal here where it's going to be a little bit more than nine is right over here. If we put the decimal here, it would be only one. If we put the decimal here, it would be 111. If we put the decimal there, it would be 1,116.

And that also makes sense. We just said we're multiplying by 10 twice and then multiplying those together. So this is 100 times bigger than whatever this should be. So if you divide by 100, you move this decimal over once—that's dividing by 10. You do it again; you're dividing by 10 again, or dividing by 100, and that's exactly where our decimal ended up.