Understanding Significant Figures: Rules, Accuracy & Loss

[Zee Student]

I had no clue where to put this, and since this is very elementary and was covered during the beginning of my physics class, I chose here.

I basically have some problems accepting some of the significant figure rules.

One problem which makes no sense:

If say 202 is divided by 356, yielding:

0.567415730337...

Now, according to the rules, since the number with the minimum amount of significant figures contains three significant figures (actually both do), we can only have three significant figures in our answer.

If I am not mistaken the purpose behind significant figures was so one would not claim to have a certain degree of accuracy when it was false. For example, if your measuring instrument is only accurate to the tenths, you shouldn't have accuracy into the millionths.

Now if in this example the measuring instrument is only accurate to the ones, what purpose does it serve to limit the significant figures of the quotient when they are all decimals?

Another question, is that I have been to a couple of websites regarding significant figures, and have found out that the rules of significant figures at times take away one digit too many from accuracy. What is going on with that?

Something as pervasive in all realms of science as significant digits has to have some uniformity. So if somebody could please shed some light on this and perhaps state some solid rules that lead to no accuracy loss or explain what is going on with the normal rules I would be most grateful.

Sorry for the elementary question, but I figure I must first learn and understand the basics inside and out before moving onto more complex things.

Thank you.

 

[Tubs]

First, you need to differentiate between the definitions of 'precision' and 'accuracy'. Though they are used interchangably in everyday language, they hold different meanings in physics. In your example of 202 divided by 356, those numbers could be declared as completely precise if haven't derived them from any measureing instrument that has a specific precision measure or uncertainty related to it. If they in fact do have three significant figures, the decimal number has three sig' fig's to account for the numbers after the third sig fig not being precise (perhaps the numbers are actually 202.6 and 356.1, but your measuring instrument can't measure that precisely).

Significant figures are mainly used with experimental data, to ensure that the precision of the results only reflect the precision of the least precise measureing tool.

As for taking away the last digit, that is the digit based on your educated guess and not directly determined by your measureing instrument.