# Converting Recurring Decimals to Ordinary Fractions

As seen in the video on “The Number System”, rational numbers consist of fractions and recurring decimal numbers. In this video, you will see how to convert recurring decimal numbers into ordinary fractions following certain steps.

In the recurring number 0,333…, step 1 is to make the recurring decimal number equal to x. Thus, x = 0,333… Then, in step 2, you have to multiply both sides of the first equation (as in step 1) with 10, as there is only one recurring digit. So, it will be 10x = 3,333…

When you have two recurring digits, you should multiply each side with 100, or you should multiply each side with 1000 if there are three recurring digits. Thus, you want to have one recurring pattern on the left-hand side of the comma.

Now, in step 3, you have to get the difference between the two equations. You can say: 10x – x = 3,333… – 0,333…. You will end up with 9x = 3, as the recurring part will be eliminated. Then, to solve x, the answer will be 3/9 and that is 1/3. Now you know how to convert recurring decimal numbers into ordinary fractions.