What if you need to represent something between 1/10th and 2/10ths without misrepresenting your precision?

Fractional measurements are way better for indicating precision than decimal. With decimal precision can only be increased or decreased by a power of 10, whereas fractional can be any level of precision - just represent the precision in the denominator.

It's more it didn't have rules. Decimal standard was used by surveyors and engineers, mechanical types. Fractional was more useful for carpenters and tradesmen, descending halves is more intuitive than descending tens, it just became custom. You can order a "big inch" ruler, ten inches in a foot, inches in tenths down too, or a caliper that displays in thousandths