Dividing decimals with hundredths

let's see if we can divide 30.2 for divide it by 0.42 and try pausing the video and and solving it on your own before I work through it so there's a couple of ways you could think about it we could just write it as 30 0.2 4 / / 0.42 0.42 but what do you do now well the important realization is is when you're doing a division problem like this if you will get the same answer as long as you multiply or divide both numbers by the same thing and to understand that we could rewrite that at rewrite this division as 30 0.42 / / 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 multiply 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 could multiply it by a hundred so let's 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're 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 of this this division problem so this is going to be 30 point 4 2 times 100 move the decimal 2 places to the right gets you 3040 - the decimal is now there if you care about it and 0.42 x 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 three thousand forty-two 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 places you could view this as 3024 we clear that 3000 and 24/40 - let me clear that and we know how to tackle that already but let's do it step by step how many times does 42 go into three well it doesn't go at all so we can move on to 30 how many times does 42 go into 30 well it doesn't 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 you're dividing by a two-digit or a multi digit number I should say so let's think about it a little bit so this is roughly 40 this is roughly 300 so how many times is 40 going to 300 well how many times does 4 go into 30 it looks likes 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 to do a little bit of regrouping here so let's see if I regroup I take a hundred 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 nine tens and I'm going to give it over here and 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 let's bring down now let's bring down the next digit let's bring down this 4 over here how many times does 42 go into 84 well that jumps out at you or hopefully a jump or it starts to that 4 it goes 2 times 2 times 2 is 4 2 times 2 times 4 is 8 you subtract and we have no remainder so 3042 divided by 42 is the same thing as 30 point 4 2 divided by 0.42 and it's going to be equal to 72 it's going to be equal to 72 actually I'd have to copy and paste that I'll just write this this is equal to 72 this is equal to 72 72 just like that