Between my first assessments I met some exercices that I don't know how to do them because I did not understand well the rules or maybe I applied in a wrong manner.

For instance:

The following numbers are expressed correct to two significant figures. Representing each number by the letter $x$, express the range in which each must lie, using an inequality.

a) 210 b) 64 c) 3.0 d) 0.88.

I don't understand what means these numbers and how to interpret that they are correct to two significant figures. It can be that 64 is an exact measured value rounded using two siginificant figures? So if $x=64$, then $$ 63.5\le x < 64.5. $$ Or 210 is an exact measure value rounded using two significant figures, so if $x=210$, then $$ 209.5\le x < 210.5. $$

Where can I find something about significant numbers and degree of accuracy? Thank you.

  • $\begingroup$ I would think that for 210, the range would be 205-215. $\endgroup$ – spaceisdarkgreen Sep 17 at 23:37
  • $\begingroup$ Can you explain why is 205-215? Thank you. $\endgroup$ – stefano Sep 17 at 23:39
  • $\begingroup$ Cause the first two digits are significant, meaning the 2 and 1. So to the nearest 10, it is 210. Just like in (b), to the nearest 1, it is 64 and in (d), to the nearest .01 it is 0.88. (Maybe it would be less confusing here to always use scientific notation. So a) 2.1e2, b) 6.4e1, c)3.0e0, and d) 8.8e-2) $\endgroup$ – spaceisdarkgreen Sep 17 at 23:49

Your understanding seems correct to me.
Here are two links that may help you out. They discuss significant figures: https://www.chem.tamu.edu/class/fyp/mathrev/mr-sigfg.html.


Good Luck!


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