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# Express \(0.12\bar{3}\) in the form p/q , where p and q are integers and q ≠ 0

**Solution:**

Given, \(0.12\bar{3}\)

We have to express \(0.12\bar{3}\) in the form p/q, where p and q are __integers__ and

q ≠ 0.

A recurring decimal is a decimal representation of a number whose digits are repeating its values at regular intervals.

The infinitely repeated portion is not zero.

So, \(0.12\bar{3}\) = 0.12333333

A number is said to be rational only if its decimal representation is repeating or __terminating__.

Let x = 0.123333

10x = 10(0.123333)

10x = 1.23333

Now, 10x - x = 1.23333 - 0.123333

9x = 1.110000

9x = 111/100

x = 111/900

x = 37/300

Therefore, \(0.12\bar{3}\) = 37/300

**✦ Try This: **Express \(0.2\bar{1}\) in the form p/q , where p and q are integers and q ≠ 0.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 1

**NCERT Exemplar Class 9 Maths Exercise 1.3 Sample Problem 2**

## Express \(0.12\bar{3}\) in the form p/q , where p and q are integers and q ≠ 0

**Summary:**

Non-terminating repeating decimals are known as the rational numbers.So the p/q form is 37/300

**☛ Related Questions:**

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