In The Sand Reckoner, Archimedes comes extremely close to discovering (inventing?) both the positional number system and some form of scientific notation: he uses the geometric sequence of powers of $10$ to express very large numbers and formulates and proves the fact that $10^m \times 10^n = 10^{m+n}$ (except that since he counts from $1$, it's a bit more messy).
Gro-Tsen
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