# Express the following in the form p/q , where p and q are integers and q ≠ 0: \(5.\overline{2}\)

**Solution:**

Given, the number is \(5.\overline{2}\)

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, = 5.2222

Let x = 5.222 -------- (1)

Multiplying by 10 both sides,

10x = 10(5.2222)

10x = 52.222 --------- (2)

On subtracting (1) and (2),

10x - x = 52.222 - 5.222

9x = 47

Therefore, x = 47/9

**✦ Try This: **Express 1.666 in the form p/q

Given, the number is 1.666

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.

Let x = 1.666 -------- (1)

Multiplying by 10 both sides,

10x = 10(1.666)

10x = 16.666 --------- (2)

On subtracting (1) and (2),

10x - x = 16.666 - 1.666

9x = 15.0000

x = 15/9

Therefore, x = 5/3

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

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

## Express the following in the form p/q , where p and q are integers and q ≠ 0: \(5.\overline{2}\)

**Summary:**

p/q form of the number \(5.\overline{2}\) is 47/9, where p and q are integers and q ≠ 0

**☛ Related Questions:**

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