How to Write a Repeating Decimal as a Fraction

Converting a repeating decimal to a fraction can initially seem challenging, but it’s a straightforward process. Here’s how to do it step by step.

Let’s take a repeating decimal as an example: 0.6666…, where the 6 repeats indefinitely.

1. Step 1: Assign the repeating decimal a variable. Let’s say: x = 0.6666…
2. Step 2: Multiply by a power of 10. Since the repeating part (6) is one digit long, we’ll multiply by 10 to shift the decimal point: 10x = 6.6666…
3. Step 3: Subtract the original equation from this new equation. Now, we will subtract x from 10x:
   10x – x = 6.6666… – 0.6666…
4. Step 4: Simplify the equation. This gives us:
   9x = 6
5. Step 5: Solve for x. Now we solve for x:
   x = 6 / 9, which simplifies to
   x = 2 / 3.

So, the repeating decimal 0.6666… can be expressed as the fraction 2/3.

This method can be applied to any repeating decimal. Just identify the repeating part and follow the steps to convert it into a fraction.