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## Rewriting decimals as fractions

Current time:0:00Total duration:2:17

## Video transcript

Write 7/8 as a decimal. And so the main
realization here is that 7/8 is the same
thing as 7 divided by 8, which is the same thing
as 7 divided by 8. These are all different ways
of writing the same thing. So let's actually
divide 8 into 7. And I'll do it down here just
so I have some more real estate to work with. I'm going to divide 8 into 7. And I'm going to add
a decimal point here, just because we know
that this value is going to be less than 1. 7/8 is less than 1. We're going to have
some digits to the right of the decimal point. And let me put the decimal
point right up here, right above the
decimal point in 7. And then we start dividing. And now this really turns
into a long division problem. And we just have to make sure we
keep track of the decimal sign. So 8 goes into-- it
doesn't go into 7 at all, but it does go into 70. So 8 goes into 70 eight times. So it goes into 70 eight times. 8 times 8 is 64. And then you subtract. 70 minus 64 is 6. And then bring down
another 0 because we still have a remainder. We want to get to the point
that we have no remainders. Assuming that this thing
doesn't repeat forever. And there's other ways
we can deal with that. 8 goes into 60? Well, let's see. It doesn't go into it eight
times because that's 64. 8 goes into 60 seven times. 7 times 8 is 56. And then we subtract again. 60 minus 56 is 4. And now, we can bring down
another 0 right over here. And 8 goes into 40? Well, it goes into 40
exactly five times. 5 times 8 is 40. And we have nothing. We have nothing left over. And so we're done. 7 divided by 8 or 7/8 is
equal to 7 divided by 8, which is equal to 0.875. But I'll put a leading 0 here
just so it makes it clear that this is where
the decimal is. 0.875. And we are done.