[lopmotr]

You really shouldn't put that 0.15 on the end. The numbers weren't that accurate to begin with so it gives the false impression that those digits mean something.

I hope it doesn't feel like I'm picking on you but I can't help myself saying something because this is a pet peeve of mine. Rounding appropriately is taught in physics class at school but I think most people don't learn that or think it doesn't apply outside of class.

[Sharlin]

Not sure why you were downvoted. The concept of significant digits is pretty important.

[zajio1am]

Or perhaps one should not assume anything about accuracy just from the numeric presentation of the value and when the accuracy is relevant, it should be mentioned explicitly (or looked for in the original source). Numeric presentation is just too vague way to represent such complex issue as accuracy.

Not rounding values after conversion has an advantage that it does not change the meaning of the claim, while rounding requires evaulating assumptions of the original claim to ensure it is done properly.

Also note that rouding of intervals is different than rounding of each of its bound value separately. If the original claim is 'the value is between 110 - 155 K', then proper rounding should be -164 - -119 degC to ensure that the original inverval is inside the new interval so the meaning of the original claim (with its implicit probabilistic assumptions) still holds, just is less accurate.

[HourglassFR]

> Or perhaps one should not assume anything about accuracy just from the numeric presentation of the value and when the accuracy is relevant, it should be mentioned explicitly (or looked for in the original source). Numeric presentation is just too vague way to represent such complex issue as accuracy.

Of course one should assume something about the acccuracy from the number of displayed digits. It's a pretty fundamental concept in physics or even engineering. You can argue that it is just a convention but then again so are numbers in the first place. When writing down a number you will have to make a choice on how many digits to write down (even if its just zeroes), so we might as well use that to convey some meaning. Yes it does not always suffice and so we can use a more elaborate notation when needed, but by default it is a useful convention.

> Not rounding values after conversion has an advantage that it does not change the meaning of the claim, while rounding requires evaulating assumptions of the original claim to ensure it is done properly.

In other words, don't try to understand the claim and just compute. It can make sense in some context but I don't generally think it is the right approach.

[diffeomorphism]

> Or perhaps one should not assume anything about accuracy just from the numeric presentation of the value

One common convention is that the value is written in a way that matches the accuracy. For example, you would never write 73.458 +/- 0.1 because the last digits are meaningless given the accuracy. Similarly, if you measure distances with a tape and round you inputs to the nearest cm, you wouldn't give areas in square mm. In turn, if you give the area in mm^2, then this implies that you think your error bounds are precise enough for this to make sense.

So it is not about readers not "assuming things" but a pretty explicit, though wrong, claim of precision on part of the previous post.

[lopmotr]

We have to assume something about the accuracy otherwise there might as well not be any numbers at all! What if it was +/- 100 K ?

Writing 2 extra decimal places is assuming the original values also have 2 decimal places with zeros in them.

It's reasonable to assume the digits the author gave are correct and there are no other unwritten zeros after them. Even if the scientists really did measure 110.00 - 155.00 K, the author of the source document decided to remove that information and we don't know what it "really" was so we shouldn't guess.

[KMag]

> Writing 2 extra decimal places is assuming the original values also have 2 decimal places with zeros in them.

As long as you have at least one digit of precision, scientific notation is unambiguous as to the number of significant figures.

[lopmotr]

Yes, but these figures weren't written in scientific notation so we can't tell. Especially the trailing 0 on 110 is ambiguous because people often write a 0 there where it really is 0 while the convention is that a 0 means it's unknown.