Significant Figures Question [ENDORSED]

[Michael_Johanis_2K]

I have a question regarding significant figures.

"Air in a bicycle pump is compressed by pushing in the handle. If the inner diameter of the pump is 3.0 cm and the pump is depressed 20. cm with a pressure of 2.00 atm, (a) how much work is done in the compression? (b) Is the work positive or negative with respect to the air in the pump? (c) What is the change in internal energy of the system?"

a) w = -P(ex) * DeltaV
= -(2.00 atm) (-pi * (1.5 cm)^2 * 20.0 cm) * (1 L / 1000cm^3 ) * (101.325 J / Latm)
= 29 J

I round to *two* significant figures because of the "3.0 cm" and I should round only at the *end*. Is this right? The book says the answer is 28 J.

Even if I round to 5 or 6 sig figs because I know that I will end with 2 sig figs (to avoid round-off error), I still get 29 J. The book got 28 J, though. What should I do?

On quizzes, the midterm, and the final, is it fine to round at each step? Or should the final answer be unrounded, but each step can be rounded just to show my work (for purposes of partial credit)?

Thank you.

[Ishita_Dubey_2D]

Generally, to avoid rounding error, you should always keep additional significant figures in your calculations and round off only the final answer. I'm not completely sure why the book has a differently rounded answer, but it could be because the editors used values for the constants with less significant figures (i.e. 101.3 J/Latm instead of 101.325 J/Latm).