# Express the following in the form p/q , where p and q are integers and q ≠ 0: \(0.\overline{001}\)

**Solution:**

Given, the number is \(0.\overline{001}\)

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, \(0.\overline{001}\) = 0.001001

Let x = 0.001001 -------- (1)

Multiplying by 1000 on both sides,

1000x = 1000(0.001001)

1000x = 001.001 --------- (2)

On subtracting (1) and (2),

1000x - x = 1.001 - 0.001

999x = 1.000

Therefore, x = 1/999

**✦ Try This: **Express \(0.\overline{01}\) in the form p/q

Given, the number is \(0.\overline{01}\)

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 = 0.0101 -------- (1)

Multiplying by 100 both sides,

100x = 100(0.0101)

100x = 1.01 --------- (2)

On subtracting (1) and (2),

100x - x = 1.01 - 0.01

99x = 1.00

x = 1.00/99

Therefore, x = 1/99

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

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

## Express the following in the form p/q , where p and q are integers and q ≠ 0: \(0.\overline{001}\)

**Summary:**

p/q form of the number \(0.\overline{001}\) is 1/999, where p and q are integers and q ≠ 0

**☛ Related Questions:**

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