Turning a Recurring Decimal into a Fraction

Let x = 0.333…

Multiply both sides by 10:

10x = 3.333…

Now subtract the original equation:

10x − x = 3.333… − 0.333…

9x = 3

So:

x = 3/9 = 1/3

Why it works

The repeating part lines up and cancels. The same idea works for other recurring decimals, though the multiplier may be 100 or 1000 instead of 10.

Useful next step: cover the worked answer and try the same method on a similar question before moving on.