suppose i have a finite numeric value less than 1 and greater than or equal to 0, like 0.231

i build a loop which, in each step:

- multiplies the value by 10
- drops the integral component so that only the fractional part remains

e.g. 0.231 → 0.31 → 0.1 → 0.

the loop finishes when the resulting value is 0

clearly this algorithm will terminate for any value in decimal space

will it also necessarily always terminate for any value in floating‐point space?