Sig Figs in 0.0 deg C

[CookingWithGas]

In reading the OP I’m assuming that 0.0[sup]o[/sup]C means that this is a measurement. But the freezing point of water (at sea level IIRC) is exactly 0[sup]o[/sup]C by definition. Is an exact measurement like that considered to have an infinite number of significant digits?

[Quercus]

@Shalmanese

I don’t like that system, it seems intuitively obvious to me that 2 measurements of the same value with different accuracies should have different sig figs.

See, your problem is that you’re expecting something rigorously logical, and the significant figures system isn’t and never will be rigorous; it’s just a short-cut approximation. People sometimes memorize certain ‘rules’ for sig figs and think it’s therefore a consistent system, but it’s not. The discussion of how many sig figs 0.0 degrees Celcius should have shown that already.

Real scientific error notation (e.g. 0.0 +/- 0.03) is consistent and theoretically sound, and in my opinion not really any harder to learn than sig figs, but YMMV.

[Jon_the_Geek]

@Quercus

See, your problem is that you’re expecting something rigorously logical, and the significant figures system isn’t and never will be rigorous; it’s just a short-cut approximation. People sometimes memorize certain ‘rules’ for sig figs and think it’s therefore a consistent system, but it’s not. The discussion of how many sig figs 0.0 degrees Celcius should have shown that already.

Real scientific error notation (e.g. 0.0 +/- 0.03) is consistent and theoretically sound, and in my opinion not really any harder to learn than sig figs, but YMMV.

I definitely agree, and, after thinking about this and some related issues, I’m going to push for teaching it that way, including sig figs as a simplified version that doesn’t always work 100% perfectly but which their instructor will likely require.

Thanks for the replies!

[scr4]

@Jon the Geek

First, I never said I intended to teach anything incorrect.

OK. I only said it because you seemed to insist that “…0.1 deg C should be thought of as having 2 significant digits in most case…” even after we explained why it’s incorrect.

@flight

I had always thought it was just as reasonable to express significant digits on Celcius as for Kelvin. You will need to convert to Kelvin for multiplication…

They are: keep the worst degree of decimal places accuracy for addition and keep the same number of sig digs for multiplication.

If you accept that as the rule, then I agree: it does work for Celsius. I think I was only taught the “keep the same number of significant digits” rule in school, and the OP seemed to only imply this rule because it asked “how many significant digits”.

[flight]

@Shalmanese

I don’t like that system, it seems intuitively obvious to me that 2 measurements of the same value with different accuracies should have different sig figs.

They do, I am not sure how you got that from my post. If I measure the distance from my desk to the wall as 2 meters with an accuracy to the meter I get:

2m

If I make the same measurement with an accuracy to the milimeter I get:

2.000m

The first has one significant digit, the second 4.

You only get oddities in sig digs when there is addition involved. In that case you are not talking about the relative precision of your measurement versus its size (which is what you are talking about with significant digits), but rather the threshold of your measuring device.