Computers work in binary, also known as base-2. So representing 1/2, 1/4 or even 3/64 can be done very accurately.
Problem is 10 is five times two (10 = 5 * 2). So to represent 1/10 accurately you need to store data in base-10. Any other base cannot store this fraction correctly.
To tag along what /r/pocok5 said – if a computer operated in trinary (base-3) it could represent 1/3 perfectly.
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