Question

Which number is irrational?

 A.0.3  B. C.0.777... D.0.454545…

Answer 1

Each of A, C, and D are rational, so presumably B is the answer here.

A is rational, since
`10*0.3=3`, so
`0.3=\frac3{10}`.

C is also rational. If
`x=0.777\ldots`, then
`10x=7.777\ldots`. This would mean
`10x-x=9x=7`, and so
`x=\frac79`.

D is rational by a similar argument. If
`x=0.4545\ldots`, then
`100x=45.4545\ldots`. So,
`100x-x=99x=45`, which means
`x=(45)/(99)=\frac5{11}`.