Is the number 0.2343434343434.. rational? Consider the following number:
$$x=0.23434343434\dots$$
My question is whether this number  is rational or irrational, and how can I make sure that a specific number is rational if it was written in decimal form.
Also, is $0.234$ rational or irrational?

We have $100x=23.434343\cdots$ and $10000x=2343.434343\cdots$ so
$$9900x=2320$$
hence $x$ is rational and
$$x=\frac{2320}{9900}=\frac{116}{495}$$
