Express \(0.12\bar{3}\) in the form p/q , where p and q are integers and q ≠ 0
Solution:
Given, \(0.12\bar{3}\)
We have to express \(0.12\bar{3}\) in the form p/q, where p and q are integers and
q ≠ 0.
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, \(0.12\bar{3}\) = 0.12333333
A number is said to be rational only if its decimal representation is repeating or terminating.
Let x = 0.123333
10x = 10(0.123333)
10x = 1.23333
Now, 10x - x = 1.23333 - 0.123333
9x = 1.110000
9x = 111/100
x = 111/900
x = 37/300
Therefore, \(0.12\bar{3}\) = 37/300
✦ Try This: Express \(0.2\bar{1}\) in the form p/q , where p and q are integers and q ≠ 0.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Sample Problem 2
Express \(0.12\bar{3}\) in the form p/q , where p and q are integers and q ≠ 0
Summary:
Non-terminating repeating decimals are known as the rational numbers.So the p/q form is 37/300
☛ Related Questions:
visual curriculum