How can I convert a repeating decimal into a fraction?

by

Converting a repeating decimal to a fraction is a straightforward process that you can accomplish with a few simple steps. Let’s break down the method:

  1. Identify the repeating decimal: Suppose you have a repeating decimal, such as 0.666…, which can also be written as 0.ar{6}.
  2. Set up an equation: Let x equal the repeating decimal. For our example, we can write it as:

    3. x = 0.666…

  3. Eliminate the repeating part: Multiply both sides of the equation by a power of 10 that matches the number of repeating digits. Since there is one digit after the decimal point here, multiply by 10:

    4. 10x = 6.666…

  4. Subtract the original equation: To get rid of the decimal, subtract the first equation from the second:

    5. 10x – x = 6.666… – 0.666…

    9x = 6

  5. Solve for x: Now, divide both sides by 9:

    6. x = 6/9

  6. Simplify the fraction: The fraction 6/9 can be simplified. Both top and bottom can be divided by 3:

    7. x = 2/3

So, 0.666… as a fraction is 2/3.

This method can be applied to any repeating decimal by adjusting the numbers accordingly. Just remember to multiply by the right power of ten for the number of repeating digits!

Leave a Comment