Express the following in the form p/q , where p and q are integers and q ≠ 0 : 0.404040…

Solution:

Given, the number is 0.404040…

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 = 0.404040 -------- (1)

Multiplying by 100 both sides,

100x = 100(0.404040)

100x = 40.4040 --------- (2)

On subtracting (1) and (2),

100x - x = 40.4040 - 0.4040

99x = 40.0000

Therefore, x = 40/99

✦ Try This: Express 0.4343 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(viii)

Express the following in the form p/q , where p and q are integers and q ≠ 0 : 0.404040…

Summary:

p/q form of the number 0.404040 is 40/99, where p and q are integers and q ≠ 0

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