# Significant figures rules

My textbook says

"Significant figures are the digits conveying meaningful information. It includes all certain and first uncertain digit. If you are given a no. like 11.2 (sf=3), then uncertainity of +_1 is understood in the last digit."

I understand that it means that first two digits '1','1' are certain and the last digit '2' is uncertain. i.e the number lies between 11.1 and 11.3.

Now, let me take some other eg. Let it be 12.0(sf=3). It means that first two digits are certain and the last one is uncertain. According to the rule, the no. should lie between 11.9 and 12.1. Also, according to the rule, first two digits are certain i.e they have fixed value(we are sure about them). They are '1'&'2' respectively, but here they have changed(12 was changed to 11). Then, there are two uncertain digits. Isn't it? It is not in accordance to my textbook rule that if there are 3 sf, then 2 digits are certain and the last sf is uncertain. How would you explain this? Is my textbook rule incomplete or wrong or am i taking it some other way?

Your textbook is incorrect, both in its categorisation of certain and uncertain digits (as you have noted) and in the value it assigns. The rule is $$\pm$$ half if no further information is given. I.e. you treat every reported value as if it has been rounded to the precision expressed. E.g. 0.12 is $$\pm 0.005$$ and 0.120 is $$\pm 0.0005$$