How do you find the repeating decimal 0.246 with 246 repeated as a fraction?
1 Answer
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:
Explanation:
Set this repeating decimal to a variable, say,
Now, multiply this by a power of
Here, the whole number changes, but what is repeating is still
The repeating decimals should cancel out:
We can finally divide by
And simplify:
Therefore,