I am a little lost regarding how to prove that a number is rational.
I am given a number $210.12$, and I have to prove that it is rational. Looking at the definition of rational numbers, it can be expressed by a fraction of two integers. In this case $$210.12 = \frac{5253}{25}$$
How do I proceed from here? Any advice and guidance will be much appreciated.
With respect to the Canonical Form of Rational Number definition $\mathbb{Q}$ $$\mathbb{Q}=\{\frac ab|a,b \in \mathbb{Z},b\neq0,(a,b)=1 \}$$ as an example $\frac68 \not\in \mathbb{Q}$ but if you simplify $\frac68$ to $\frac34$ there is $(3,4)=1\\(6,8)\neq1$
so $\frac34 \in \mathbb{Q}$ .
hope it helps you