Expressing numbers in p/q form

We have to convert decimals into p/q

We know that there are three types of decimal expansions

1. Terminating
2. Non-Terminating Repeating
3. Non-Terminating Non-Repeating

For Terminating numbers,

Eg: 0.125

We just remove the decimal point, and divide by as many 0 as the number of digits after decimal

Since, 0.125 has 3 digits after decimal point, we remove the decimal point and divide by 1000

So, 0.125 = 125/1000

For Non-Terminating Repeating numbers

If we are given an expansion like

  0.2353535…….

How do we express it in p/q?

Let us look at an example

For Non-Terminating Non Repeating numbers

We know that Non-terminating, non-repeating numbers are irrational numbers.

And they cannot be expressed as p/q