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 $10\times0.3=3$, so $0.3=\dfrac3{10}$.

C is also rational. If $x=0.777\ldots$, then $10x=7.777\ldots$. This would mean $10x-x=9x=7$, and so $x=\dfrac79$.

D is rational by a similar argument. If $x=0.4545\ldots$, then $100x=45.4545\ldots$. So, $100x-x=99x=45$, which means $x=\dfrac{45}{99}=\dfrac5{11}$.