The significant figures of a number are those digits that carry meaning contributing to its accuracy. For decimal numbers any zeros before the first non-zero digit are not significant, but any after the last non-zero digit are included to indicate that they are significant.
0.00123 — 3 significant figures
0.12300 — 5 significant figures
Multiplication and division: the result should have as many significant figures as the input number with the fewest significant figures.
e.g. 0.058 x 0.0124 = 0.00072 (not 0.0007192)
Addition and subtraction: the result should have as many decimal places as the input number with the fewest decimal places.
e.g. 0.465 + 0.8453 = 1.310 (neither 1.3103 nor 1.31)
Integers (for reference)
All the calculations here involve decimal numbers, and avoid integers. This is because without further information it is not clear how many significant figures there are in an integer such as 9200 (most probably two, but there could be three or even four). In actual practice the number of significant figures would need to be indicated in some way.
Exact Numbers (for reference)
An ‘exact number’ is a number (usually an integer) which is known with complete certainty, e.g. five people, duplicate experimental readings. As an example, consider calculating the average height from measurements on five people. We would only consider the precision of the values of the heights in determining the number of significant figures in the result.