Converting fractions to decimals
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.