How to Convert Recurring Decimals to Fractions (Proportions Part 6/6) (2026/27 exams)?

Converting recurring decimals to fractions is like turning a never-ending song into a simple tune you can sing along to.

Imagine you have a decimal that repeats forever, like 0.333..., where the 3 keeps going and going. You want to find out what fraction makes this repeating decimal, just like finding out how many slices of pizza make up a whole pie.

Here's the trick: let’s call your recurring decimal something simple, like x. So if we say x = 0.333..., then multiply both sides by 10 (because there’s one repeating digit), you get 10x = 3.333...

Now subtract the original equation from this new one:

10x - x = 3.333... - 0.333...

That gives you:

9x = 3

Then, divide both sides by 9, and you find that x = 3/9, which simplifies to 1/3.

So just like turning a long song into one simple note, or a repeating decimal into a neat fraction, this method helps you make sense of something that seems endless.