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# Fraction to decimal with rounding

Sal writes 16/21 as a rounded decimal. Created by Sal Khan.

Video transcript

Lets see if we can express 16 over 21 as an decimal Or we can call this sixteen twenty first. This is also sixteen 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 we're going to have some less than one, so lets add some decimal places here. We're going to round to the nearest thousandths in case our digits just keep going on and on and on. And let's start dividing, 21 goes into 1 zero times, 21 goes into 16 zero times. 21 goes into 160, well, 20 would go into 160 8 times, So let's try 7, lets see if 7 is the right thing. 7 times 1 is 7, 7 times 2 is 14 and then when we subtract, we should get a remainder less than 21. If we picked the largest number here that goes into the largest number here, that 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, I did it in my head right there, but you could re-group, you could say that 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 zero. Now lets bring down a zero 21 goes into 130, so lets see, would 6 work? It looks like 6 would work 6 times 21 is 126, so that looks like it works. So lets put a 6 there 6 times 1 is 6 6 times 2 is 120. There's a little bit of an art to this. Alright, now let's subtract. Once again, we can regroup, this would be a 10, we've taken 10 from essentially this 30, so this becomes a 2 10 minus six is 4 2 minus 2 is zero 1 minus 1 is zero. Now let's bring down, now lets bring down another zero 21 goes into 40, well, almost 2 times but not quite, so only 1 time. 1 times 21 is 21, and now lets subtract This is a 10, this becomes a 3. 10 minus 1 is 9 3 minus 2 is 1 and we're going to have get this digit because we want to round to the nearest thousand. So if this is 5 or over we're going to round up if this is less than 5 we're going to round down. So let's bring another 0, lets bring another lets bring another zero down here and 21 goes into 190, lets see I think 9 will work Lets try 9, 9 times 1 is 9 9 times 2 is 18, when you subtract 190 minus 189 is 1 And we could keep going on and on but we already have enough digits to round to the nearest thousand. This digit right over here is greater than this is greater than or equal to 5, so we will round up in the thousandths place. So if we round to the nearest thousandths, we can say that this is 0.76 and then this where we're going to round up, 762.