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Decimal divisors in the hundredths place can be a little confusing. In this video we'll show you how to move the decimal and make it a whole number. Pretty nifty! Watch. Created by Sal Khan.
Video transcript
Lets see if we can divide 30.24 divided by 0.42 and try pausing the video and 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, divided by 0.42 0.42 but what do you do now? well the important realization 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 we can rewrite that rewrite this division as 30.42 over, (Sal meant 30.24 here) 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 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 could 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 one, so we're not changing the value of this fraction or you could view this (as a) 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 all 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 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 about 7 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 im 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, 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 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 (out at you) or... it goes (into 84) two times. 2 times 2 is 4 2 times 4 is 8 you subtract and we have no remainder so 3042 divided by 42 is the same thing as 30.42 divided by 0.42 and its going to be equal to 72 (note: 3042/42 does not equal 72, Sal made a mistake) its going to be equal to 72 actually I didn't have to copy and paste that I will just write this this is equal to 72 (72.42857) this is equal to 72 72 just like that.