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 | 10th 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 | 10th Jun, 2014, 10:29: PM

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