Recurring digits
"One thing I had to do to be able to do this, was change how I saw the overbar notation. Instead of just meaning 'then you write that series of digits forever and that's the rest of the number', you see it as an infinite series of whatever's under it, divided by the number base one more time in each term. That itself is a number that can be multiplied or divided by the base (moving it left or right on the page) or added to smaller numbers written after it. Then, digits with overbars can be processed like other digits, and expanded only at the end if necessary." ~me on Discord, on the server "the best way to count", channel #general-1.
I've come up with a few tricks to aid in the arithmetic of rational numbers, using the overbar notation for recurring decimals.
New features:
- overbarred digits before other digits
- overbarred digits before the radix point
- stacked overbars
- overbarred digits with expansion multipliers
Useful techniques:
- step-by-step unrolling
Properties:
- de facto smaller bases for overbarred numbers
- relationships with numbers like 9, 99, 98, 999 etc
- overbars with expansion multiplied by the radix