Question

# Check whether the number 0.318564318564318564….. is rational or irrational.

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Solution

## 0.318564318564318564...=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯318564. It is non – terminating and recurring, hence it is a rational number. Also, we can check by the following method : x=0.318564318564318564...(i) Multiplying both sides by 1000000, we get 1000000x=318564.318564318564...(ii) Subtracting (i) from (ii), we get 99999x=318564 ⇒x=31856499999 We can see that x can be represented in the form pq where p and q are both integers and q≠0. Hence, x= 0.318564318564318564... is a rational number.

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