If TINYINT can store three characters, for example, why can't it store up to the number 999?
Because it takes only 8 bit and hence can encode no more than 2^8 = 256 values.
The three characters you see in something like '123' are the result of the binary to decimal conversion. You cannot store arbitrary 3 characters there.
It is 8 bits and can actually store a maximum value of 255. 8 bits have 256 possible states including zero.
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