We’ve grown used to a full-decimal system, but all kinds of weird stuff has existed in the past.

Telugu (a language of southern India) has an interesting traditional numeric system: base ten for integers, and base four for fractions.

   U+0C78 "౸" TELUGU FRACTION DIGIT ZERO FOR ODD POWERS OF FOUR
   U+0C79 "౹" TELUGU FRACTION DIGIT ONE FOR ODD POWERS OF FOUR
   U+0C7A "౺" TELUGU FRACTION DIGIT TWO FOR ODD POWERS OF FOUR
   U+0C7B "౻" TELUGU FRACTION DIGIT THREE FOR ODD POWERS OF FOUR
  (U+0C66 "౦" TELUGU DIGIT ZERO is used for even powers of four too)
   U+0C7C "౼" TELUGU FRACTION DIGIT ONE FOR EVEN POWERS OF FOUR
   U+0C7D "౽" TELUGU FRACTION DIGIT TWO FOR EVEN POWERS OF FOUR
   U+0C7E "౾" TELUGU FRACTION DIGIT THREE FOR EVEN POWERS OF FOUR

Seems complicated at first, but in practice it’s roughly just: circle for zero, and tally marks for one, two and three, alternating vertical and horizontal.

Few Telugu speakers even know about this any more—no one can read even the traditional integers (౦౧౨౩౪౫౬౭౮౯), because 0123456789 have replaced them. (This is the case in most but not all Indian languages. Bengali’s traditional digits are still common, so you can enjoy ৪ being four and ৭ seven.)

A couple of articles and discussions about it:

• https://www.unicode.org/wg2/docs/n3156.pdf is the best public resource I know of (Unicode proposals and related papers are often delightful for information on obscure written stuff, because they had to write down and publish the details to get the characters encoded). One tid-bit: NYSE used a similar decimal/quaternary system until early 2001.

• https://blog.plover.com/math/telugu.html from the same site as the current article, discussed in https://news.ycombinator.com/item?id=14683767 nine years ago.

Egyptian Fractions (2006)