Well, what do you mean by decimals?

Take, the Sumerians for example. If you look at Babylonian Texts from c. 2000 BC, they wrote numbers smaller than ones using their base 60 system (sexagesimal). So if you wanted to write one half, they would write "30" since 30 is half 60 (although obviously not in the Hindu numerals I am writing, but in cuneiform). Note that they had no special symbol to indicate this is not 30, or 1800 (= 60 * 30), this was decided purely from context, since they did not treat zero as a number. So if you wanted to write 72 and a half, Babylonians wrote 1 12 30 = 60 * 1 + 1 * 12 + 30 * 1/60. Is that a fraction? Is it a decimal?

We see this today in how we do degrees of a circle: for instance, Baghdad is at 33°20′N 44°23′E where a "minute" is 1/60th of a degree, and also in time (1 hour = 60 minutes = 60 * 60 seconds).

Contemporary Egyptians used continued fractions, where they only accepted fractions of the form 1/n, where n is a whole number. This is fine, until you want to do some operations on fractions. So Egyptians could write 1/5th, but what about 2/5ths? Well, they wrote it as 1/3rd + 1/15th (obviously). This took a lot of work, and arithmetic books throughout the Greek influenced world (the Greeks inherited both systems from Babylon and Egypt, but seemed to have preferred the Egyptian system) spent chapters and chapters on how to use these fractions.

We should note that Egyptians and Greeks didn't write fractions like I've been writing them, with a numerator and a denominator, but with a variety of special symbols. Chinese scholars beginning sometime before c. 100 BC (I've seen texts using this that early, but I don't know what the oldest known is) used a system much like ours, and eventually Indian mathematicians did as well beginning in the 7th century, which then spread to Europe by the 15th century. I'm skipping over a lot of details, if you want to see a transitional system, look at Fibonacci's Liber Abaci, where he uses a system that is sort of like what we were taught in school but different enough to be utterly confusing.

If you want a decimal system that looks like ours, you have to go to Chinese mathematics in the 4th century BC, which I believe was also non-positional, like Babylonian, but I'm not sure (Chinese mathematics is a big gap in my knowledge). I think it must be non-positional, because you need zero to do that, which hadn't quite developed in India by that time, but I read that it all has to do with counting rods, which I also don't know much about. I do know that "dot" decimal notation (positional, with zeros) was used by Arabs in the 10th century, and was popularized in Europe much later by Simon Stevin a Flemish writer and mathematician in the 16th century.

So it depends on what you mean. If you insist on something that looks like what you were taught in school, then decimals are much later. If you want to count the Babylonian system, then I would argue we don't really have enough evidence either way.

Hope that helps.

Edited to fix some typos and unclear wording.