wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
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 q0.
Hence, x= 0.318564318564318564... is a rational number.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Irrational numbers
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon