We have to convert decimals into p/q
We know that there are three types of decimal expansions
- Non-Terminating Repeating
- Non-Terminating Non-Repeating
For Terminating numbers,
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
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