Question

3.24 (4 being repeated) to a fraction

Answer 1

146/45

Explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

`x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=(29.2)/(9)=\boxed{(146)/(45)}`

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Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.