Questions about Significant Figures and working with them?

Question

I have a few questions about significant figures (sig figs)

Using a meter stick to measure a table which is about two meters long, the actual measurement is 1818 mm. Should I only accept the first three digits, making the final answer 1820 mm? What is my extimated error, +/- 1mm?

Also take the length of the table, say it is 645 mm. Would the error estimation still be: +/-1mm or possibly less?

(Remember I am using a meter stick for all measurements)

When finding the area, what numbers would I compute and would I keep only 3 sig figs?

Using the 3 sig fig #'s, I come up with:

1 173 900 mm^2

Would that be the correct answer, and if it is what is my error percentage?

Thank you.

Answer 1

1.) If your meterstick actually measures mm, then your answer is 1818, unless you've been told to specifically round to 3 significant figures. The error estimation would be +/- 1 mm in both instances.

2.) When continuing calculations, do not round to significant figures until the very end. You would multiply 1818 * 645, not 1820 * 645, and then you would take the final area calculation and round to 3 significant figures (because of 645 mm).