CBSE Class 9 Answered
Is 1.1111... a rational number or irrational?
If it is a rational number, then how can we classify non terminating decimals as rational or irrational? Please explain.
Asked by Arkajyoti Banerjee | 10 Jun, 2014, 12:12: AM
Expert Answer
1.111...... is an rational number, since it is repeating.
It can be expressed in the form of p/q where p and q are integers and q not equal to0.
let x = 1.111111..... (i)
10x = 11.111111..... (ii)
Subtracting (i) from (ii)
9x = 10
x = 10/9
Hence,
1.11111..... = 10/9
So in general, if we can express the non terminating recurring decimal in the form of p / q then it is a rational number or else it is an irrational number
Answered by Dharma Teja | 10 Jun, 2014, 10:29: PM
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