# Express the following in the form p/q , where p and q are integers and q ≠ 0: \(0.1\overline{34}\)

**Solution:**

Given, the number is \(0.1\overline{34}\)

We have to express the number in p/q form.

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, \(0.1\overline{34}\) = 0.13434

Let x = 0.13434 -------- (1)

Multiplying by 1000 on both sides,

1000x = 1000(0.13434)

1000x = 134.3434 --------- (2)

Multiplying by 10 on both sides,

10x = 10(0.13434)

10x = 1.3434 ------------ (3)

On subtracting (2) and (3),

1000x - 10x = 134.3434 - 1.3434

990x = 133

x = 133/990

Therefore, x = 133/990

**✦ Try This: **Express \(0.\overline{21}\) in the form p/q

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

**NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 7(vi)**

## Express the following in the form p/q , where p and q are integers and q ≠ 0: \(0.1\overline{34}\)

**Summary:**

p/q form of the number \(0.1\overline{34}\) is 133/990, where p and q are integers and q ≠ 0

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