# How To Convert Decimal Numbers To Fractions Hi, I’m Peter Edwards from Bluetutors. We
teach children of all ages, right from primary school to degree level and we find the highest
quality tutors. And today I’m going to teach you some maths. We’re now going to look at how to change a
decimal into a fraction. And so we’re going to start off with a fairly simple example
and hopefully expand that into something a bit more complicated. So if we look at the
first example we have up here, 0. 12. So what you have to think about when you’re
converting this to a fraction is how many decimal places do we have. In this case, we
have two. The first decimal place represents tenths
and the second represents hundreds. So, this in fact is equal to 12/100. And we can simplify
that by dividing top and bottom by four to get 3/25. So this decimal here, 0.12, is equal to 3/25.
So let’s do a similar thing with this decimal now. In fact, you can see we have four decimal
places. So we have tenths, hundredths, thousandths, and ten thousandths. So this is going to be
equal
to 7524/10000. And so again we can simplify that. This might
take me a while. So we’ll divide top and bottom by two first to give us 3762/5000 which is
equal to 1881/2500. And so that is that fraction simplified. Now,
we’re going to look at a more complicated situation where we have a decimal but these
two dots here mean that that line of digits is repeated over and over again. This is a
recurring decimal which never ends and we’re going to try and work out what fraction this
is. Now, the way to do that is to take this and
in fact, multiply it so that this decimal point comes after this seven here. So we need
the point to jump six times. So we’re going to multiply this by one million. So we’re going to call this number here ‘x’
and we’re going to say 1,000,000 times x is equal
to 142857.142587. And again this recurs over
and over again. Now we have this, what we can do is take our
other x
and what we’re going to do now is take this bottom line away from this top line. That
leaves us with 999999x equal to 142857. And so x is equal to 142857/999999. And if you put that into your calculator and
work it out, you will see that that is equal to 1/7. And so that is how to work out a fraction
when you have a recurring decimal. And as long as it is a recurring decimal and not
an irrational number, then you’ll always be able to that. And that is how to convert decimals into fractions.
.

### 15 thoughts on “How To Convert Decimal Numbers To Fractions”

• January 14, 2012 at 5:37 pm

omg it was that simple

• May 23, 2012 at 8:33 am

you need to explain how you reduced large numbers dude!

• July 23, 2012 at 8:37 pm

Exactly what I was thinking. This has confused me, it's taught me nothing. I'm going to look for a video which explains things more clearly.

• March 13, 2013 at 4:51 pm

This sounded like a math love story haha

• April 23, 2013 at 9:52 pm

the dude looks gay he suxs

• September 5, 2013 at 2:03 am

thanks love 😉

• September 5, 2013 at 2:05 am

Wtf is wrong with you. He took time of his life to try and teach shit to you, its offered help which means that if you don't get it ask or rewatch it, and if you don't like it, fuck you, because its help not a request.

• October 2, 2013 at 12:29 am

Smartie pants

• October 16, 2013 at 12:17 pm

……………………………..

• October 16, 2013 at 12:17 pm

• November 17, 2015 at 1:13 am

i didnt understand you sir ,sorry can you say clear

• February 2, 2016 at 4:00 pm

How did you get 999999?

• December 20, 2016 at 10:40 pm

what the hell is the music for? horrible, you are supposed to be teaching maths not music

• December 14, 2017 at 2:07 pm
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