How Do You Round Numbers When Calculating Significant Figures?

[triden]

Homework Statement

This topic is causing me some slight confusion and I have a few questions I would like to get resolved.

When you have a number say like: 0.0800, I would assume that it is 3 sig figs...right? Now say I were to divide it by oh..I don't know..517 (which is also 3 sig figs), I would get an answer of: 0.000154738

Since both of the input numbers are 3 sig figs, I would assume to round the product to 3 sig figs. If you do that you get 0.000155. To me, this number looks like non-sense because I am at a higher precision than what I started with - I am getting more data than what I had to begin with.

What would I do in this case? What would I round the product to?

One other Question. Is it possible to round 598 to two sig figs? Would it just be 600, or am I way off base? To me 600 only really has 1 certain sig fig.

Thanks

 

[ideasrule]

0.000155 only seems more precise because it's a smaller number. In actuality, it represents an error margin of roughly 0.1%, as do 517 and 0.0800. It's the percent error that significant units are supposed to represent.

As for 598, one way to express it to 2 sig figs is 6.0 *10^2. That's ridiculous, however; don't worry about it. Significant figures are only a teaching tool meant to make students understand the concept of accuracy, and have limited applications in formal science. In real science and engineering, +- error bars are used. 598 might be 598 +- 5, for example, or 598 +- 10, depending on the actual accuracy of the instrument used.