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
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