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How To Change Decimals To Fractions

How To Change Decimals To Fractions

Bluetutors more than delivers on changing decimals into fractions. Beyond the basics, this short film will also show how to convert a recurring decimal into a fraction.

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. .