Significant Figures: Why Leading Zeros Don't Count

[Svein]

I am not saying 'add' in the way that I actually add the number of significant figures with the precision. I'm saying it in a figuratively way.
The more significant figures you have in the decimal places, the more precision you have.

Or is this wrong?

If the person doing the measurements knows what he/she is doing, the number of significant figures given represents the precision of the measurement. If not (see my earlier anecdote about introducing a lot of figures when converting from one standard to another), the number of "significant" figures are neither significant nor bear any relation to the measurement precision.

 

[jbriggs444]

I am not saying 'add' in the way that I actually add the number of significant figures with the precision. I'm saying it in a figuratively way.
The more significant figures you have in the decimal places, the more precision you have.

Or is this wrong?

That idea is correct. A better word choice might be "related".

 

[RaduAndrei]

Significant figures do not add to precision. They express the precision in a different way.

Ok. I finally understood it. (with the help of the book introduction to error analysis by Taylor)

A measured value with n significant figures means an uncertainty of one unit in the nth significant figure. Sometimes it means a bigger uncertainty, sometimes it means a smaller uncertainty, depending on the situation. But we adopt a middle of the road definition that it is one unit.

An uncertainty of one unit in the nth significant figure means some variable precision depending on the number (here precision is defined as uncertainty/measured value). So for 10, the precision is 10%, while for 99 the precision is 1%. We can say that the precision is roughly 50%.

In general for n sign figures, the precision can vary from 10^(-n+3)% to 10^(-n+2)%.

Thus, there is an approximate correspondence between the number of significant figures (as we defined them) and the precision (as we defined it) given by:
roughly precision [%] = 10^(-n+3)/2 %

PS: Also we adopted the convention that all trailing zeros are significant.