Question

Why is our percentage system out of 100?

Answer 1

"Cent" in per_cent_ means 100. So the word literally means "per 100". You can also describe portions on other ways (fractions, decimals, specific words like half and quarter, etc) but percentages became popular and stuck because having a common way to compare portions makes things easier.

Essentially though, it's just a number. It's nice because it's bigger than 10 so have more granularity and you don't have to use decimals as often (e.g. 85% instead of 8.5 tenths). But it's not so big like 1000 that you too much unneeded granularity, although per 1000 is an actual thing called per mille and uses the symbol "‰". It's just not very popular though. Basis points (per 10000, ‱) is a common unit though and often used in things like interest rates and stock price changes.

Answer 2

As said by other people percent comes from the fact that cent means 100 so literally means per 100.

One of the things I love about the Chinese language is that they use the word 分之 （fen zhi) for fractions and percentages so 百分之 is percent but just says out of 100, you can also says stuff like 三十三分之 which is out of 33.

Just a fun fact I know.