What empire discovered the decimal system?

Answer 1

Decimal system is a vague term in this respect. Technically it refers to the use of a 10 digit number system (base-10, 0-9). But I suspect you are asking about the use of the decimal.

The first meaning: it's origin is not known with certainty. China (first) and India (second) both seem to have developed a decimal system independently of one another. So, both are given credit.

The second meaning (technically referred to as decimal fractions. They are fractions whose denominator is a multiple of 10 i.e. -> 4.22387): The origin of this is the same. More or less, the Chinese in the 1st century BC. An Indian mathematician also used it. From him, it spread to the Middle East (Likely where it was combined with the Arabic number set we use now) and finally to Europe.