I'm looking at binary data representations for fractions, and I was wondering what kind of a data structure the fraction would have if you were to store both the numerator and denominator that store a fraction. Is it just two separate numbers that have no relation but are combined when used in a calculation?
If you want to store rational numbers without losing precision the correct way is to store both the numerator and denominator.
In practice most people use either floating-point math or built-in/library arbitrary-precision number data-types (e.g. Java's BigDecimal).
If you specifically want to use a data-type for fractions, some languages have built-in types for rational numbers. For most other languages there is usually a library with a usable datatype (e.g. for Java Apache Commons has a Fraction class and for C/C++ GMP has a mpq_t datatype)