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# Fraction to decimal with rounding

CCSS.Math:

## Video transcript

let's see if we can express 16 over 21 as a decimal or we could call the 16 21st this is also 16 divided by 21 so we can literally just divide 21 into 16 and because 21 is larger than 16 we're going to get something less than 1 so let's just literally divide 21 into 16 and we're gonna have something less than 1 so let's add some decimal places here we're going to round to the nearest thousandth in case in case our digits keep going on and on and on and let's start dividing 21 goes into 1 0 times 21 goes into 16 0 times 21 goes into 160 well 20 would go into 168 times so let's try 7 21 let's see if 7 is the right thing so 7 times 1 is 7 7 times 2 is 14 and then when we subtract it we should get a remainder less than 21 if we pick the largest number here that goes into the largest number here where if I multiply it by 21 I get close to 160 without going over and so if we subtract we do get 13 we do get 13 so that worked 13 is less than 21 and you could just subtract it I did in my head right there but you could regroup you could say this is a 10 and then this would be a 5 10 minus 7 is 3 5 minus 4 is 1 1 minus 1 is 0 now let's bring down a 0 21 goes into 130 so let's see would 6 work it looks like 6 would work 6 times 21 is 126 so that looks like it works so let's put a 6 there 6 times 1 is 6 6 times 2 is 120 there's a little bit of an art to this all right now let's subtract and once again we can regroup this would be a 10 we've taken 10 from essentially this 30 so now this becomes a 2 10 minus 6 is 4 2 minus 2 is 0 1 minus 1 is 0 now let's bring down now let's bring down another 0 21 goes into 40 well almost 2 times but not quite so only one time 1 times 21 is 21 and now let's subtract this is a 10 this becomes a 3 10 minus 1 is 9 main three minus two is one and we're going to have to get this digit because we want to round to the nearest to the nearest thousandth so this if this is over if this is five or over we're going to round up if this is less than five we're going to round down so let's bring another zero let's bring another zero down here and 21 goes into 190 let's see I think nine will work let's try nine 9 times 1 is 9 9 times 2 is 100 or is 18 when you subtract 190 minus 189 is 1 and we could keep going on and on and on but we already have enough digits to round to the nearest thousandth this digit right over here is greater than this is greater than or equal to 5 so we will round up in the thousands place so if we round to the nearest thousandth we can say that this is 0.76 and then this is where we're going to round up 7 6 to