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# Fraction to decimal with rounding

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

Video transcript

Let's see if we can
express 16/21 as a decimal. Or we could call this
16 twenty-firsts. 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 going to have
something less than 1. So let's add some
decimal places here. We're going to round to the
nearest thousandths in case our digits 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 eight times. So let's try 7. 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 where, if I multiply it by
21, I get close to 160 without going over. And so if we subtract,
we do get 13. So that worked. 13 is less than 21. And you could just subtract it. I did it 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 another 0. 21 goes into 40, well,
almost two 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. 3 minus 2 is 1. And we're going have
to get this digit. Because we want to round
to the nearest thousandth. So if this is 5 or over,
we're going round up. If this is less than 5,
we're going to round down. So let's bring
another 0 down here. And 21 goes into 190. Let's see, I think 9 will work. Let's 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, and on. But we already
have enough digits to round to the
nearest thousandth. This digit right over here 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 is where
we're going around up-- 762.