You theoretically shouldn't even have to be a computer scientist. A standard mathematical education ought to teach you that for any given base, the only numbers that can be represented in that base exactly are numbers where the prime factorization of the denominator contains only prime numbers that are also contained in the prime factorization of the base itself, or is simply 1 for integers. Base 10 has 2 and 5. .2 is 1/5, so it's precise. .5 is 1/2, so it's precise. 1/12 has 2 2s in it, which works, and a 3, which doesn't, so 1/12 is recurring.

But prime factorization seems to be taught for almost superstitious reasons, as some sort of math trick rather than a fundamental aspect of understanding numbers at even the most basic of levels, with neither students nor teachers nor the curriculum writers really understanding why this is in the lesson plan, so, yeah, I suppose you have to be some sort of super expert genius to swiftly realize that 1/3 can't be represented in a base-2 number. But it shouldn't be that way.