Consider imprecise numbers. In normal usage, one can assume some leeway with the unstated digits, so e.g.
permits any number in the range [370.25, 370.35[. However, final zeroes offers a small problem here, as 370 can be imagined to be 37 * 10 or 37.0 * 10, giving us the following possible ranges:
A jargon for some mathematically inclined profession, or the language of a highly technological culture could potentially include these distinctions in their spoken numbers by having a significant zero. This significant zero would appear in the same kinds of constructions giving higher numbers as do regular numbers, with the exception that it only appears once, at the least digit position that is significant (not the least significant such).
Thus, you'd get numbers like zeronty, zero hundred, zero thousand, and these would cut off the number at the desired level of precision.
The tens would in addition need two tens - one that is just ten, the other is ten and zero.
Thus ten thousand would signify 'ten +/- 500', 'ten and zero' would signify 'ten +/- 50', and ten thousand zeronty would signify ten thousand +/- 5, and finally 'ten thousand zero' would signify ten thousand +/- 0.5.
Smaller fractions could also be formed using the regular ways fractions are formed.