Check sibling questions

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


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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.