1m and 1000mm are not the same length.

1000mm and 1.000m are the same length.

the only thing significant figures seem to be optimizing for is debate about the right way to use significant figures

in my experience, it’s always better to eschew them entirely and simply write an explicit error margin

Well, you wouldn't write 1.000m on it either.

That one would certainly lead to you getting something other than you are trying to design. Unless the machinist misreads it, or it gets assigned to that one machinist that likes searching people out and talking to them.

Not according to https://en.m.wikipedia.org/wiki/Significant_figures

You're right that I'm remembering my sig-fig rules wrong, but you're not entirely right:

> Zeros to the right of the last non-zero digit (trailing zeros) in a number with the decimal point are significant if they are within the measurement or reporting resolution.

> 1.200 has four significant figures (1, 2, 0, and 0) if they are allowed by the measurement resolution.

and

> Trailing zeros in an integer may or may not be significant, depending on the measurement or reporting resolution.

So my first example "1m and 1000mm" actually might be the same length, depending on if those zeros are significant or not which has not been clearly communicated.

My second example "1000mm and 1.000m" is also ambiguous, since 1.000m is clear(ish) about its sig-figs, while 1000mm is not. I suppose I could have written "1000. mm"

Best solution imo would probably be:

- something that actually specified the error: 1m ± 0.0001m

- or using words to indicate what's meant: "exactly 1000mm"

The classic solution to this ambiguity is to always use scientific notation.

The sig figs in 1.0E3mm, 1E3mm, or 1.000000E3mm are unambiguous.

Pretty close. If they added an additional zero to make 1.0000 meters they would be the same number of significant figures technically. But it's all convention. I've been in classes where 1.000 would be 4 significant figures.

> 120.0000 consists of six significant figures (1, 2, and the four subsequent zeroes) except for the last zero If the resolution is to 0.001.

1.000 has 4 significant figures. Absent other context, 1000 has 1.

When arguing convention, everyone is right, and everyone is wrong.

I don’t think this is correct.

1000.0 mm would be the same as 1.000m (or is it 1.0000?).

1000m has ambiguous sig figs.