How do you find the repeating decimal 0.246 with 246 repeated as a fraction?

1 Answer
Dec 15, 2017

Set the decimal as a variable to be multiplied by a power of ten (such that the repeating decimal part remains the same), then subtract the original from the multiplied number, and simplify as needed to get:
0.246246246... = 82/333

Explanation:

Set this repeating decimal to a variable, say, N.

N = 0.246246246...

Now, multiply this by a power of 10, one that keeps the decimal part of the number the same:

1000N = 246.246246246...

Here, the whole number changes, but what is repeating is still 246. We can then subtract the original from the multiplied number:

1000N - N = (246.246246246...) - (0.246246246...)

The repeating decimals should cancel out:

999N = 246

We can finally divide by 999 to get our answer:

(999N)/999 = 246/999

N = 246/999

And simplify:

N = 82/333

Therefore, 0.246246246... = 82/333