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Calculate with fractions in different place value systems and with Roman numerals

What would our world look like if we didn't do calculations using the decimal system with its ten digits, but rather a different place value system? What would the keyboards of our devices be like if the duodecimal system with its twelve digits, the Maya system with twenty digits (for fingers and toes), the hexadecimal system with the 16 digits 0 to F or an exotic place value system such as one with seven digits became established would have?

This app provides a calculator for fractions that can be switched between different place value systems. As an additional treat, there is also a conversion function for Roman numbers. Roman numerals behave similarly to the decimal system for whole numbers, but the Romans preferred a division into twelve for fractional numbers.