Multiplying decimals word problems

- [Instructor] We are told James dog weighs 2.6 kilograms. And Hao's dog weighs 3.4 times as much as James dog. How much does Hao's dog weigh? Pause this video and try to figure that out. Well, Hao's dog is 3.45 times the weight of James' dog, which is 2.6. So we just have to multiply 3.45 times 2.6. So 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. So 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 three times four, that would be around 12. So this should be someplace between six and 12. And to think about what this is, 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 gonna 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 five times six is 30, four times six is 24 plus three is 27, three times six is 18, plus two is 20. And now let's go to the tens place. So I'll put a zero there 'cause I'm dealing with the tens, two times five, and let me cross these out, don't need these anymore, two times five is 10, regroup that one, two times four is eight, plus one is nine, two times three is six. And now let me add up all of this business. I get 0, 7, 9, 8. So if this has the same digits, 8, 9, 7, 0, where do we think we're gonna put the decimal? If it was two times three, we'd get to six. If it was three times four, we'd get to 12. So it'd be in between those. So the only place to put the decimal here, that'd be in between six and 12 would be right over there. But why does that make sense? Well, one way to think about it is to go from 3.45 to 345, we would have to multiply by a hundred. We'd have to move this decimal over to the right twice every time you're multiplying by 10, and 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 ones. So if you're multiplying by 100 and by 10, this thing right over here is gonna be 100 times 10 larger than this thing, or this is gonna be 1,000 times larger than this. So if you wanna figure out what this is going to be, you just need to divide by 1,000. So you divide 10, by 100, by 1,000, 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 six and 12. It shouldn't be 89 or 897 or 0.8 or 8,970. Let's do another example. Ben rides his electric scooter for 1.2 hours at a speed of 9.3 kilometers per hour. How many kilometers does he ride in all? Pause this video and see if you can figure that out. So once again, we're just gonna multiply these decimals. We're gonna have 1.2 times 9.3, and we could do the same idea. Let's just think about it without the decimals first. So 12 and 93, and it is good to think about this to go from 1.2 to 12, you have to multiply by 10, and they go from 9.3 to 93 you also have to multiply by 10. And so once I take this product, whatever the answer's 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 gonna be 100 times bigger than whatever answer should be over here. So to go back, we could divide by 100. Another way to think about it is we can estimate. This is 1.2 times 9.3. So a little bit more than one times a little bit more than nine. 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. Three times two is six, three times one is three. This is turning into a bit of a song. Now we'll go to the 10th place, nine times two is 18, and then nine times one is nine, plus one is 10. And I'm gonna add all of that together and I'm going to get six plus zero, six, three plus eight is 11, regroup the one, one plus zero is one. And then we just bring this one down. And 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. And 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'd be only one. If we put the decimal here, it would be 111. If we put the decimal there, it'd 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.