[Cyrustorz]

I calculated the density of my substance to be 2.7 g/cm^3, and then I calculated my range of error to be 0.08.

However, does it make sense to say "2.7 +- 0.08 g/ cm^3" when my error range has an additional decimal point of accuracy than my listed density???

Would I instead have to round my range of error to 0.1 so that I can say "2.7 +- 0.1 g/cm^3"??

[Borek]

You should either use significant figures or give the density and the error. If the error is ±0.08 (whatever you mean by that) I would report the result as 2.xx±0.08 or even 2.xxx±0.0xx. As far as I am aware there are no set rules saying how many digits should be listed, but more than 2 would be probably excessive.

[Cyrustorz]

You should either use significant figures or give the density and the error. If the error is ±0.08 (whatever you mean by that) I would report the result as 2.xx±0.08 or even 2.xxx±0.0xx. As far as I am aware there are no set rules saying how many digits should be listed, but more than 2 would be probably excessive.

My problem is that a measurement I used to calculate density was limited to two significant figures so I can't do 2.xx for density.  However, listing error with absolute error calculation, etc. is required. So should I round to 2.7 +- 0.1 g/cm^3?

[Corribus]

How did you determine the error? If you just took, e.g., the standard deviation of 3 measurements, each with a precision of 0.X, then I don't like reporting an error (standard deviation) with 0.XX precision. In that case, I would round to whatever is the precision of your instrument.

Using the word "error" without defining what you mean by it makes it difficult to offer help.

[Cyrustorz]

How did you determine the error? If you just took, e.g., the standard deviation of 3 measurements, each with a precision of 0.X, then I don't like reporting an error (standard deviation) with 0.XX precision. In that case, I would round to whatever is the precision of your instrument.

Using the word "error" without defining what you mean by it makes it difficult to offer help.

My instrument for measuring mass had 0.X precision, but my instrument for volume had 0.0X precision. Which is why I rounded my density only to 2.7, but what does that mean for my error calculation?

[mjc123]

When you multiply or divide two quantities, you should add the relative errors. Thus if you have, say, a relative error of 2% in the mass and 3% in the volume, the relative error in density is 5%. (Which in this case would be 0.135, or 0.1 if we're rounding to 1 dp.)

My instrument for measuring mass had 0.X precision

This means it was limited to one decimal place, not two significant figures. How many sf depends on the absolute mass, e.g for 4.6 g it would be 2 sf, but for 46.3 g it would be 3 sf. That's why it's a good idea to do the relative error calculation as above, and round to the appropriate sf at the end.

[Corribus]

Typically we propagate the error as the root of the sum of the squares of the errors, not a simple addition.

[Arkcon]

I calculated the density of my substance to be 2.7 g/cm^3, and then I calculated my range of error to be 0.08.

However, does it make sense to say "2.7 +- 0.08 g/ cm^3" when my error range has an additional decimal point of accuracy than my listed density???

Would I instead have to round my range of error to 0.1 so that I can say "2.7 +- 0.1 g/cm^3"??

You see, this entire thread, I've had a problem understanding your application of significant figures.  Leading zeros are never significant.  The example is given here: https://en.wikipedia.org/wiki/Significant_figures#Identifying_significant_figures  You know your error to one significant place only, and may only report your measurement to one significant figure.  That is: 3 ± 0.08

[Borek]

You know your error to one significant place only, and may only report your measurement to one significant figure.  That is: 3 ± 0.08

I don't like this approach. When using significant figures by "3" we typically mean something between 2 and 4, and by 3.0 something between 2.9 and 3.1. Giving the result as 3±0.08 means the error is useless.

In general, the idea of mixing error calculated by any means with significant figures is asking for troubles, this is a good example of why.