Question

Give the periodic decimal representation of each of the following rational numbers :A) 2/3 B) 5/7 C) 9/11 D) 118/55

Answer 1

Given,

The rational numbers are:

`(A)(2)/(3)\text{ }(B)(5)/(7)\text{ }(C)(9)/(11)\text{ }(D)(118)/(55)​`

The decimal representation is 2/3 is,

`(2)/(3)=0.666666666`

The decimal representation is 5/7 is,

`(5)/(7)=0.714285714285`

The decimal representation is 9/11 is,

`(9)/(11)=0.818181818`

The decimal representation is 118/55 is,

`(118)/(55)=2.145454545`

Hence, the periodic representation of the rational numbers is obtained.