Significant Digits in Measurements and Computations

[HussanAli]

Hey fellows I have read a number of books on Significant figures but I am not able to understand what are these. One confusing thing is that eg. If I take length of wire with a meter rod (with 1 meter minimum length measureable) & found it to be 7 meters. Then according to rule of Significant figure there must be some error in measurement & measurement must be within 6-8 meters. Please someone give explanation of this.

 

[LowlyPion]

Welcome to PF.

The issue is more in the expression of the length than in the meter stick you are using. While the finest scale may be 1 meter in your example, the observer may reasonably estimate to say 1/4 of that and your uncertainty could be expressed as ± 1/4 if more % precision is useful.

On the other hand if you have a measure that is 1000 m long, and it is only marked, in 1 m increments, then a ± 1 m may be satisfactory precision for the kinds of measurements you would be making.

In other words, I think some common sense needs to used in actual practice.

 

[minger]

To elaborate a little more on the previous post, significant figures are also used in computations. They basically say that your final answer can only be as accurate as the least accurate number used.

For example, let's say that I need to divide 2.3069 by 4. (side note, integers are always assumed to have "infinite" significant digits, you'll understand more here in a second). Anyways, the answer is 0.576725. However, with significant digits, we say that due to the precision of what came in, the answer can only be 0.5767. Basically, how can we get more precision than what we started with.