If you have a material sample with measured length of 1cm ±0.5cm, and a measured mass of 3g±0.5g, then reporting 3.3333333333g/cm for mass per unit length is just lying. It's between 0.14 and 0.6, so "about 0.3g/cm" is not lying, whereas "0.333333333333g/cm" is.

What do you think about 0.333 ± 0.222 g/cm?

0.3 (-0.2+0.3) g/cm would be more correct. You've still got 3 significant figures when the inputs only had 1. Just don't lie, it's not that hard.

Interesting definition of a "lie". I don't think anything about that is inaccurate or untruthful. At best it could be called verbose, but yours is actually no shorter. Confidence intervals supersede significant figures in all respects, and now you've introduced a small but unnecessary bias that depends on the peculiarities of base 10.

This is the issue that is addressed by paying attention to "significant figures." Digits that are significant are shown. Those that aren't, aren't. It's appropriate to round where your precision ends.

business ppl ~always~ prefer that approach.

When we go to industry or "the real world", it's as if we are forced to unlearn all good practices