eurekameh said:The lab procedure instructed us to record the number of swings in 60 seconds using a PASCO counter. We did this for three trials. Let's say that I recorded 80, 81, and 80 swings. I want to take the average number of swings. (80+81+80)/3. How many sig. figs do I keep?
cepheid said:The whole point of sig figs is to represent the uncertainty in measured values. What's the precision of a "PASCO counter?" If it only reports counts to the nearest whole number, then obviously it makes no sense to report any decimal places, since you would be over-representing the certainty of your measurement.
Borek said:I think the question was not about expressing the integer result that comes from the counter, but the averaged value from the several trials - if so, decimal points are perfectly OK, as the result should be reported as average±sigma.
Or am I wrong?
Significant figures are the digits in a number that are known with certainty, plus one digit that is estimated. They are important because they indicate the precision or accuracy of a measurement or calculation. They help ensure that the reported value is not misleading or falsely precise.
To determine the number of significant figures in a number, count all the non-zero digits and any zeros between them. Trailing zeros after a decimal point are significant, but leading zeros are not. Zeros at the end of a whole number may or may not be significant, depending on whether they are used to indicate precision or just to fill in space.
Significant figures can be frustrating because they can be tricky to work with and understand. They also require careful attention to detail and can lead to errors if not used correctly. Additionally, different rules for significant figures may be used in different fields of science, causing confusion and frustration.
When performing calculations with significant figures, the final answer should have the same number of significant figures as the number with the fewest significant figures in the calculation. For multiplication and division, the final answer should be rounded to the same number of significant figures as the number with the fewest significant figures. For addition and subtraction, the final answer should be rounded to the same number of decimal places as the number with the fewest decimal places.
Some common mistakes when dealing with significant figures include rounding too early in a calculation, using too many or too few significant figures in a calculation, and not understanding when to use trailing zeros as significant. It's also important to remember that significant figures are a representation of precision, not accuracy, and should not be used to compare the accuracy of different measurements.