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### Course: Class 7 (Old)>Unit 2

Lesson 7: Dividing decimals

# 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.

## Want to join the conversation?

• When you divide decimals is it the same as when you divide numbers above 1?
• Yes, just multiply the smaller number by 10 until it is a whole number, and then multiply the other number by 10 the same amount of times. Them divide with those numbers and you will get the answer.
• At Sal changes the division into a fraction. In any video does he then simplify the fraction to make the division easier? An example is: 3024/42 are both even so it's divisible by 2/2 equaling 1512/21. Then that's divisible by 3/3 equaling 504/7. Finally, divide by 7/7 to equal 72. It may take more steps, but each division is by a single digit which is easier to do.
• There is no 'proper' way. True understanding of this concept (diving by decimals) means you can look at the problem in more than one way and select the most appropriate. rhsobon is not suggesting his way is 'better'. It's different. It's worth considering. I would also be interested to see a video where this alternative way of tacking the problem was explored. I echo rhsobon's question: is there one?
• for the division equation u typed 3024 instead of 3042
• That is a known error in the video. If you are not watching in full screen mode, you see a correction box that pops up.
• cant u just take out the decimals and then do the long division
• Yes and that is exactly how you should approach these types of problems. Just remember to add the decimal back into the problem when you finish.
• Sal wrote 3042 instead of 3024. I just noticed tht at the very end. Even Sal makes mistakes.
• Yes, but there is a team of volunteers who look for Sal's mistakes, and they are corrected such as the text box at around .
• , there has been an error.please take note
• Do not know what error you are talking about, but Sal makes an error at :46 when he writes 30.42 instead of 30.24 which has a text box correction that continues until end of video. At he is just talking about dividing and the fact that 42 cannot go into 3 or 30, so you have to go all the way to 302.
• Did he just stutter? -
• Pretty sure he did.
• we all know sal got something wrong but its not like he cant get anything wrong, he only human after all.
• you switched numbers what
• what if you have a number like 390.4 and 0.61 do you add a zero to 390.4 so then 0.61 can become a whole number?
• Yes, you would change them into 39040 and 61 so both numbers are changed by two digits to the right.
(1 vote)

## 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.