If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Rewriting tricky fractions to decimals

## Video transcript

I'll now show you how to convert a fraction into a decimal and if we have time maybe we'll learn how to do a decimal into a fraction so let's start with what I would say is a fairly straightforward example let's start with the fraction 1/2 and I want to convert that into a decimal so this the what the method I'm going to show you will always work what you do is you take the denominator and you divide it into the numerator let's see how that works so we take the denominator is 2 and we're going to divide that into the numerator 1 and you're probably saying well how do I divide 2 into 1 well if you remember from the dividing decimals module we can just add a decimal point here and add some trailing zeroes right we haven't actually changed the value of the number but we're just getting some precision here we put the decimal point here 2 goes into 1 does this to go into 1 no 2 goes into 10 so we go 2 goes into 10 5 times 5 times 2 is 10 remainder 0 we're done so 1/2 is equal to 0.5 let's do a harder slightly harder one let's figure out one-third well once again we take the denominator 3 and we divide it into the numerator and I'm just going to add a bunch of trailing zeroes here 3 goes into well 3 doesn't go into 1 3 goes into 10 three times 3 times 3 is 9 subtract get a 1 bring down the 0 3 goes into 10 three times and actually this decimal point is right here 3 times 3 is 9 okay do you see a pattern here we keep getting the same thing as you see it's actually 0.33 3 3 it goes on forever and a way to actually represent this if obviously you can't write an infinite number of threes is you could just write point well you could write 0.33 repeating which means that the 0.33 will go on forever or you could actually even say 0.3 repeating although I tend to see this more often maybe I'm just mistaken but in general this line on top of the decimal means that this these this number pattern repeats indefinitely so 1/3 is equal to 0.33 3 3 3 and goes on forever and that's equal to another way of writing that is 0.33 repeating let's do a couple of maybe a little bit harder but they're they all follow the same pattern let me pick some weird numbers let me say let me she do an improper fraction let me say 17 over 9 so here it's interesting the numerator is bigger than denominator so actually we're going to the number larger than 1 but let's let's work it out so we take 9 and we divide it into 17 and let's add some trailing zeroes for the decimal point here so 9 goes into 17 one time 1 times 9 is 9 17 minus 9 is 8 bring down a 0 9 goes into 80 well we know 9 times 9 is 81 so it has to go into it only 8 times because can't go into 9 times 8 times 9 is 72 80 minus 72 is 8 bring that another zero I think we see a pattern forming again 9 goes into 80 eight times 8 times 9 is 72 and clearly I could keep doing this forever and we keep getting eighths so we see 17 divided by 9 is equal to one point eight eight where the point eight eight actually repeats forever or if we actually wanted to round this we could say that that is also equal to one point depending where we wanted to round it what place we could say you know roughly 1 point 8 9 or we could round at a different place I round it in the hundreds place but this is the actually the exact answer 17 over 9 is equal to one point eight eight actually I do a separate module but how would we write this as a mixed number well well actually I'm gonna do that in a separate I don't want to confuse you for now let's do a couple more problems let me do a real weird one let me do seventeen over 93 what does that equal as a decimal well we do the same thing 93 goes into Ceph I make a really long line up here because I don't know how long how many decimal places will do and remember it's always the denominator being divided into the numerator let's usually confused me a lot of times because you're often dividing a larger number into a smaller number so 93 goes into 17 zero times right there's a decimal 93 goes into 170 goes into it one time one times 93 is 93 170 minus 93 is 77 bring down the zero 93 goes into 770 let's see it'll go into it I think roughly eight times times 3 is 24 8 times 9 is 72 plus 2 is 74 and then we subtract 10 6 is equal to 26 let me bring down another 0 9 3 goes into 26 probably sees about 2 times 2 times 3 is 6 18 this is 74 zero so we could keep going this is actually we could keep figuring out the decimal points you could do this indefinitely but if you want to at least get an approximation you would say 17 goes into 93 point or 17 over 93 is equal to 0.18 - and then the decimals will keep going and you could keep doing it if you want if you actually saw this in exam they probably tell you to stop at some point you know round it to the nearest hundredths or thousands place and let this just so you know let's let's try to convert it the other way from decimals to fractions actually this is this is I think you'll find a much easier thing to do if I were to ask you what 0.035 is as a fraction well all you do is you say well 0.035 that is the same thing as we could we could write it this way we could write that's the same thing as well let me that's the same thing as 0 3 well I shouldn't write 0 3 5 that's the same thing as 35 over 1,000 and you're probably saying Sal how did you know it's 35 over a thousand well because we went to 3 this is the tens place the tenths not tens this is hundreds this is a thousandths place right so we went to three decimals of significance so this is 35 thousandths if the if the decimal was let's say if it was point zero three zero there's a couple of ways we could say this well we could say oh well we got to three we went to the thousands place so this is the same thing as 30 over a thousand or we could have also said well point zero three zero is the same thing as point zero three because this zero really doesn't add any value like it so if we have point zero three then we're going to the hundredths place so this is the same thing as 3 over 100 so let me ask you are these two the same well yeah sure they are if we divide both the numerator and the denominator of both of these expressions by 10 we get 3 over 100 well let's go back to this case are we done with this is 35 over 1000 I mean it's it's right that is a fraction 35 over a thousand but if we wanted to simplify it even more it looks like we could divide both the numerator and the denominator by 5 and then just just to get it into simplest form that equals 7 over 200 and if we wanted to convert 7 over 200 into a decimal using the technique we just did so we we do 200 goes into seven and figure it out we should get 0.035 I'll leave that up to you as an exercise hopefully now you get at least a initial understanding of how to convert a fraction into a decimal and maybe a vice versa and if you don't just do some of the practices and I will also try to record another module on this or another presentation have fun with the exercises