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Dividing decimals with hundredths

Dividing decimals can be made simple by multiplying both numbers by the same amount to eliminate decimals. For example, when dividing 30.24 by 0.42, multiply both by 100 to get 3,042 divided by 42. Using long division, the final answer is 72, making the process easy and efficient. Created by Sal Khan.

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Video transcript

Let's see if we can divide 30.24 divided by 0.42. And try pausing the video and solving it on your own before I work through it. So there is a couple of ways you can think about it. We could just write it as 30.24 divided by 0.42. But what do you do now? Well the important realization is, is when you're doing a division problem like this, you will get the same answer as long as you multiply or divide both numbers by the same thing. And to understand that, rewrite this division as 30.42 over 0.42. We could write it really as a fraction. And we know that when we have a fraction like this we're not changing the value of the fraction if we multiple the numerator and the denominator by the same quantity. And so what could we multiply this denominator by to make it a whole number? Well we can multiply it by 10 and then another 10. So we can multiply it by a 100. So lets do that. If we multiply the denominator by 100 in order to not change the value of this, we also need to multiply the numerator by 100. We are essentially multiplying by 100 over 100, which is just 1. So we're not changing the value of this fraction. Or, you could view this, this division problem. So this is going to be 30.42 times 100. Move the decimal two places to the right, gets you 3,042. The decimal is now there if you care about it. And, 0.42 times 100. Once again move the decimal one, two places to the right, it is now 42. So this is going to be the exact same thing as 3,042 divided by 42. So once again we can move the decimal here, two to the right. And if we move that two to the right, then we can move this two to the right. Or we need to move this two to the right. And so this is where, now the decimal place is. You could view this as 3,024. Let me clear that 3024 divided by 42. Let me clear that. And we know how to tackle that already, but lets do it step by step. How many times does 42 go into 3? Well it does not go at all, so we can move on to 30. How many times does 42 go into 30? Well it does not go into 30 so we can move on to 302. How many times does 42 go into 302? And like always this is a bit of an art when your dividing by a two-digit or a multi-digit number, I should say. So lets think about it a little bit. So this is roughly 40. This is roughly 300. So how many times does 40 go into 300? Well how many times does 4 go into 30? Well, it looks like it's about seven times, so I'm going to try out a 7, see if it works out. 7 times 2 is 14. 7 times 4 is 28. Plus 1 is 29. And now I can subtract. Do a little bit of re-grouping here. So lets see, if I regroup-- I take a 100 from the 300. That becomes a 200. Then our zero tens, now I have 10 tens, but I'm going to need one of those 10 tens, so that's going to be 9 tens. And I'm going to give it over here. So this is going to be a 12. 12 minus 4 is 8. 9 minus 9 is 0. 2 minus 2 is 0. So what I got left over is less than 42, so I know that 7 is the right number. I want to go as many times as possible into 302 without going over. So now lets bring down the next digit. Lets bring down this 4 over here. How many times does 42 go into 84? Well that jumps out at you, or hopefully it jumps-- It goes two times. 2 times 2 is 4. 2 times 4 is 8. You subtract, and we have no remainder. So 3,042 divided by 42 is the same thing as 30.42 divided by 0.42. And it's going to be equal to 72. Actually, I didn't have to copy and paste that, I'll just write this. This is equal to 72. Just like that.