I like the formula you give for volume. I don't think I have seen it in junior high and high school level textbooks regularly. It does seem to steer clear of the problem. In math books of course the V=pi*r^2*h is the formula used as far as I know (maybe it is intuitively derived from area of...
Consider this:
If a person measures the diameter as 12.0 cm and the height as 13.0 cm and uses the volume formula generally taught, maintaining the rules of significant figures, he would have to report his answer as 1.47x10^3 cm^3 because the original measurement has 3 significant figures. If...
Here is quote from this site http://www.astro.yale.edu/astro120/SigFig.pdf
"General guidelines for using calculators
"When using a calculator, if you work the entirety of a long calculation without writing down any intermediate results, you may not be able to tell if a error is made and...
Right. So if we keep with the rule, I have to discard the example and tell the students that it is incorrect to say that 12.0 cm divided by 2 is 6.0 cm (in order to match the precision of the measuring instrument). I have to stick with the significant figures from the original measurement. I...
You've heard of "reduction to absurdity" I'm sure. Hypothetically, if I had a stack of 123 objects that measured 1.27 mm, each would share equally and be 0.010325203252... mm. Of course the problem here it is a repeating decimal so we now have an infinite number of significant figures if we...
Okay. Thanks for the answer. I've seen that rule about exact numbers in a number of places. This problem is not original to me, I'm just trying to decide how to resolve the issue in my own mind of how 12.0 divided by 2 can result in an answer 6.00 which has an unjustified significant figure...
I understand that the correct number of significant figures should be tracked throughout the calculation process (even when rounding is done at the end). Here is the essence of my question. When the number of significant figures required actually adds unmerited precision to the measurement...
Not trying to be hard to get along with but 1) I don't believe I used the word "rounding" until after you brought it up. "Estimation" is of course something that the scientist is allowed to do to give a best judgment on where the measurement falls between the calibration marks to allow another...
But "round once at the end" doesn't address the fact of the loss of a significant figure when dividing a measured number by a number of infinite precision. This was my original question.
So what your saying is that a "tally" of the significant figures at the end of each step should be kept in the margin (or some other convenient place) and rounding should be done after the last calculation to the number of significant figures that have made it through to the end? (12.0 divided...
If we allow 6.00, that definitely is higher precision than the original instrument. I think that you can't go beyond 6.0 because even dividing by a perfect 2 cannot increase precision regardless of the rules about significant digits. It seems incorrect to say that your original instrument...
I came across a significant figures problem today that I need information on. The problem is this: "What volume of water can a cylindrical container hold of it is 13.0 cm tall and 12.0 cm in diameter? Show your work and express the answer in scientific notation using significant figures."
Of...
I see what you are saying. I guess that since the polar jet is not near ground level, I assumed that the circulation had already risen and reversed direction returning southward.
I've seen diagrams that show the polar jet as actually residing in the upper northern part of the Ferrel Cell rather than the upper southern part of the Polar cell. In other words it forms in the region that the circulation begins to turn southward after rising. I can see that there is a more...
Why does the polar jet stream flow counter-clockwise around the Earth (as viewed from the north pole)? It seems that since the air at the north end of the Ferrel Cell and the south end of the Polar Cell rises, the Coriolis effect would cause a circulation in the clockwise direction.