Use of appropriate significant figures
While it is important to know how accurate a measurement is, it
is also important to convey one's degree of confidence in the accuracy
of a number when making an observation or carrying out a calculation.
This can be accomplished by noting numerical observations or quoting
results to the correct number of significant figures.
e.g. weighing the same object with different balances: Analytical balance: Weight = 2.1234 ± 0.0001 g Pan balance: Weight = 2.1 ± 0.1 g
Often the ± value is dropped, and it is understood that the number quoted has an uncertainty of at least 1 unit in the last digit. All digits quoted are called significant figures. Note that the last digit included is the one with an uncertainty of ±1.
Rules
 All nonzero digits are significant.
For example: 123. (3 sig figs)
 Zeros between nonzero digits are significant.
For example:
12.507 (5 sig figs)
 Zeros to the left of the first nonzero digit are not significant.
For example:
1.02 (3 sig figs)
0.12 (2 sig figs)
0.012 (2 sig figs)
 If a number ends in zeros to the right of the decimal point, those zeros are significant.
For example:
2.0 (2 sig figs) 2.00 (3 sig figs) {This signifies greater accuracy.}
 If a number ends in zeros to the left of the decimal point,
those zeros may or may not be significant.
For example:
If we make a statement that the weight of an object is 120 g,
how do we convey our knowledge of whether the balance was accurate
to ± 1 g or ± 10 g?
Answer: The ambiguity can be removed by using exponential notation. The weight can be expressed as 12. x 10^{1} g or 1.2 x 10^{2} g if we wish to quote unambiguously to 2 sig figs, and 12.0 x 10^{1} g or 1.20 x 10^{2} g if we have a confidence level extending to 3 sig figs.
Note: We cannot write 120.0 g since this requires known accuracy
of ± 0.1 g.
These rules apply to measured quantities which are nonexact. If
you are told that a number is exact then there is no uncertainty; i.e., the number is good to an infinite number of sig figs. Exact integers fall in this category.
An important example of an exact quantity is the coefficient of a reagent in a chemical reaction. This number, called the stoichiometric coefficient, expresses the specific number of molecules of reagent A which undergo reaction with a specific number of molecules of reagent B. The stoichiometric coefficients are exact.
2 H_{2} + O_{2} > 2 H_{2}O
Calculations with numbers having different accuracies
Multiplication or Division: the result can have no more sig figs than the least accurate number. For example:
If an object has mass of 29.1143 g and a volume of 25.0 cm^{3}, then its density is given by

Density = 29.1

143 g = 1.164572 g cm^{3} = 1.16 g cm^{3}


^{ }25.0

cm^{3}

Addition or Subtraction: the result must be reported to the same number of decimal places as the number with the fewest decimal places. For example:
19.

2 g

0.

4745 g

127.

g

SUM = 146.

6745 g = 147. g because one weight is known only to the nearest 1 g!

NOTE: Round off numbers only at the END of calculations; otherwise, errors may be inadvertently carried through.
