Question

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

Answer 1

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`