Is there any name or symbol for rational numbers with a bounded amount of decimals? As the title says, is there any name or symbol for rational numbers with a bounded amount of decimals?
For example, for the set of rational numbers that are multiples of $0.01$ (with two digits after the point; or equivalently, the subset of rational numbers that can be written using 100 as denominator), is there any specific mathematical symbol or concise way to name that?
 A: Correct me if I'm wrong, but I think in your question you meant to use the phrase, finite number of digits rather than bounded amount of decimals.
As amWhy pointed out in the comments, a terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.
As for your final paragraph, I would refer to that set as "The set of all numbers with exactly two digits after the decimal point".
Or, if you don't mind $5.670$ being in your set, seeing as it has the same value as $5.67$, then as JMoravitz pointed out, you could instead write this set more concisely as $\frac{1}{100} \mathbb{Z} = 0.01\mathbb{Z}.$ However, if you consider $5.670$ and $5.67$ to be different numbers because you care about accuracy for example in chemistry, or you really only want to allow numbers with exactly two numbers after the decimal point in your set for whatever reason you may have, then this definition will not do, because $5.670 \in \frac{1}{100} \mathbb{Z},$ but $5.670 \notin$ { all numbers with exactly two digits after the decimal point }.
