Question

Is 9.68 with the 8 repeating rational

Answer 1

Hello Mate!

Ans : Yes, number x = 9.688888...... is rational number.

Why?

Take x = 9.6888....... and multiply 10 from x

10x = 96.888.......

10x = 96 + 0.888.......

[ Let y = 0.888..... ---(i)
10y = 8.888.... ----(ii)
(ii) - (i) => 10y - y = 8.888..... - 0.888....
y = 8 / 9 ]

10x = 96 + 8 / 9

10x = ( 864 + 8 ) / 9

x = 872 / 90

Have great future ahead!

Note: Teminating and non - terminating but repeating numbers are always rational.