Show that `0. 2353535. . .=0. 2 bar 35`can be expressed in the form `p/q`, where p and q are integers and `q!=0`.

Explanation

To show that \(0.2353535\ldots = 0.2\overline{35}\) can be expressed in the form \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\), we will follow these steps:

### Step 1: Define the repeating decimal
Let \(x = 0.2353535\ldots\)

### Step 2: Eliminate the non-repeating part
To eliminate the non-repeating part (the digits before the repeating part), we multiply \(x\) by \(10\):
\[
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