Express the following in the form p/q , where p and q are integers and q ≠ 0: \(5.\overline{2}\)
Solution:
Given, the number is \(5.\overline{2}\)
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, = 5.2222
Let x = 5.222 -------- (1)
Multiplying by 10 both sides,
10x = 10(5.2222)
10x = 52.222 --------- (2)
On subtracting (1) and (2),
10x - x = 52.222 - 5.222
9x = 47
Therefore, x = 47/9
✦ Try This: Express 1.666 in the form p/q
Given, the number is 1.666
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 = 1.666 -------- (1)
Multiplying by 10 both sides,
10x = 10(1.666)
10x = 16.666 --------- (2)
On subtracting (1) and (2),
10x - x = 16.666 - 1.666
9x = 15.0000
x = 15/9
Therefore, x = 5/3
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 1
NCERT Exemplar Class 9 Maths Exercise 1.3 Problem 7(iii)
Express the following in the form p/q , where p and q are integers and q ≠ 0: \(5.\overline{2}\)
Summary:
p/q form of the number \(5.\overline{2}\) is 47/9, where p and q are integers and q ≠ 0
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