To get rid of the repeating decimals there’s a trick. The trick is to subtract that number from 10-times of itself. The first step is to write this: 10x – x = 9x. The second step is to replace “x” with the decimal number to convert. This process can be repeated with any number. To summarize:

1). Let x be the decimal number you want to convert

2). Multiply by 10, represent it like 10x

3). Subtract x from 10x.

4). Solve for x

Let’s convert 0.333… (repeating forever decimal number) into a fraction. Let x = 0.333… Then 10x =3.333…. because when you multiply by 10, you move the decimal over to the right by one. 10x – x = 9x. We calculate that 10x – x = (3.333… – 0.333…) = 3. See now we have nice whole numbers. Did you see how that algebra worked? The final step is solve for x. We have 9x = 3. All we’ve got to do is to divide both sides by 9. We then get x = 3/9. We simplify by dividing 3 and 9 by 3 to get x = 1/3. which is equal to 0.333…