# Significant digits question

## Homework Statement

1) how do I know if the significant digit is supposed to be of " infinite sig-digs" ? If it is a constant value that is universally known, ike density then i understand that. But lets say i were to do ...

35+273.15

## The Attempt at a Solution

when adding, you go to the least amount of decimal places. so does that mean I just use a whole number?

Whole numbers, given without the decimal point, usually indicate that they are completely exact, which would mean an infinite number of zeros after the decimal point. So treat them accordingly. If you see, on the other hand, 35.00 or something like that, that would mean only the first two digits after the decimal point are known accurately.

My textbook says otherwise. says that hte number 843 has 3 significant digits, so 35 has 2 sig digs, so i count them. rite?

The book may be formally right. Practically, there is an ambiguity because the method "by the book" is no good for exact whole numbers, which do occur in practice. In a formula for kinetic energy, for example, there is "2", and that "2" is exact. No one is going to write that as 2.(0) which is probably the right way by the book.

How do I know if a number has unlimited significant digits? Do values of density and molar mass have unlimited sigdigs? Do I ignore them?

Significant digits are, in my opinion, closely related to the accuracy of the answer. Let's play with the number 25, for example:

25 has two significant digits. Adding zeros in front of 25, i.e. 025 or 0025, does not add any significant digits as it doesn't have any practical meaning.

An answer of 25 could mean anything greater or equal to 25 and less than or equal to 25.4999. Hence, if you instead write 25.0, you add another significant digit, as you give a closer indication of what the answer really is, as 25.0 means that the answer is smaller than 25.04999ad instead of 25.499999.

In response to the last part of your question, any exact number could thus be said to have unlimited significant digits (although this has no practical meaning). 25 could be written as 25.00000000000000000000000 (infinity of zeros).

Depends what the "35" in your equation really represents. If it represents a physical quantity then it surely comes with an experimental error and the 5 should be considered a least significant digit. If, on the other hand, it comes from some exact mathematical calculation, then it is a mathematical constant and it has "infinite number of significant figures".

I dont know. someone else told me density/molar masses and exact mathmatical quantitiesdo not have infinite sig-digs. So I guess ill just red omy math and carry them along

Is the 35 the numerical value of some quantity (like t ) that is represented by a letter in your formula?

yess it is

Then, it was measured by a thermometer in Celsius degrees and has a finite precision.

Borek
Mentor
At the same time 273.15 is an example of an exact value.

I should remark that "the number of significant digits" notation is by no means unambiguous. When one needs to denote the true accuracy in a number, it can be done, for example, through the ± notation. E.g., 35 ± 10^-5. The ± notation is also not the ultimate answer; the accuracy may be unsymmetrical, and there is also some notation to express that.

Bottom line, use common sense when given some numbers no matter how they are expressed. If in doubt, ask.

I would say something that many people might disagree with. I think the asymmetrical uncertainty interval is something that is forced upon by people doing fitting in experimental particle physics, and trying to get more information than is actually available from a scattering experiment.