CHEMISTRY Mass and significant figures! Help!?

Question

I have a tough question for chemistry that I need help with.

Here it goes:

Suppose that a series of measurements have shown that the mean mass of an object is 122.4g with a standard deviation of 1.3g.How many significant figures are justified in the mean and how would you report the most probable mass of the object? Explain.

:o

Answer 1

When determining the number of significant figures to report, the last significant digit is the first uncertain digit.  In your case, the uncertainty is in the ones place, so the mean should be expressed as 122 +-1 g.  So three significant figures are justified since the uncertainty lies in the ones place.  There is no need to express a number beyond its uncertainty--done all the time in commercials, "Lose 5.366 % more body fat with money waster pill X!"

Also, some people choose to keep an extra insignificant figure as a subscript.  So that would be 122.4 +- 1.3 g with the tenths place digits (.4 and .3, respectively) on the mean and the standard deviation expressed as subscripts.  

This is probably all that is required but, for your own edification, higher confidence intervals could be used to express more and more probable ranges of masses (more than one standard deviation).  In keeping sig-figs though, how I explained counting them based on the standard deviation is good stuff.  Still these confidence intervals are still a function of standard deviation, so its all related (and you'll see more later in chem)!!!