# Show that 0.2353535... = 0.235 can be expressed in the form of p/q, where p and q are integers and q is not equal to zero.

The problem is based on the conversion of decimal numbers to a rational form.

## Answer: 0.2353535... = 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero.

Let's proceed with the conversion thereby establishing the proof of the given statement.

**Explanation:**

A rational number can have two types of decimal representations (expansions):

- Terminating
- Non-terminating but repeating

0.2353535... is a non-terminating but repeating decimal, it is denoted by \(0.2\bar{35}\).

let x = 0.2353535...

100x = 235.353535...

100x - x = (235.353535...) - (2.353535...)

99x = 233

x = 233/99

Therefore, 0.2353535... = 0.235... = 233/99 can be expressed in the rational form.

### Thus, 0.2353535...= 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero

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