Proof of an injection

Question

How do I construct an injection from rational numbers $\mathbb{Q}$ to integers $\mathbb{Z}$? I need to write a proof and I'm not sure how to format it.

Answer 1

Write $q \in \mathbb Q$ as $s \frac ab$, where $s=\pm 1$ and $a,b \in \mathbb N$ coprime. Then send $q$ to $s 2^a 3^b$.