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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