How To Convert Repeating Decimals To Fractions 9 Steps

Once your equation is written, you will multiply it by 10^y, where y equals the number of repeating digits in the pattern. [2] X Research source In the example of 0. 4444, there is one digit that repeats, so you will multiply the equation by 10^1. For a repeating decimal of 0. 4545, there are two digits that repeat, and you would, therefore, multiply your equation by 10^2. For three repeating digits, multiply by 10^3, etc.

In the example where x = 0. 4444, then 10x = 4. 4444. With the example x = 0. 4545, there are two repeating digits, so you multiply both sides of the equation by 10^2 (which equals 100), giving you 100x = 45. 4545.

10x – 1x = 4. 4444 – 0. 4444 On the left side, you have10x - 1x = 9x. On the right side, you have 4. 4444 – 0. 4444 = 4 Therefore, 9x = 4

On the left side of the equation you have 9x ÷ 9 = x. On the right side of the equation you have 4/9 Therefore, x = 4/9, and the repeating decimal 0. 4444 can be written as the fraction 4/9.

In the example of 4/9, that is the simplest form.

For example, take the number 6. 215151. Here, 6. 2 is non-repeating, and the repeating digits are 15. Again take note of how many repeating digits there are in the pattern, because you will multiply by 10^y based on that number. In this example, there are two repeating digits, so you will multiply your equation by 10^2.

100x – x (= 99x) = 621. 5151 - 6. 215151 (= 615. 3) Therefore, 99x = 615. 3

615. 3 x 10 / 99 x 10 = 6153/990 Reduce the fraction by dividing the numerator and denominator by the highest common factor, which in this case is 3, giving you x = 2,051/ 330[10] X Research source