Significant figures are an important aspect of doing calculations in both chemistry and physics. Significant figures allow a reader to know how precise certain calculations are and how much of a variation there may be in an answer.
First, we need to be able to identify how many significant figures are in a number. The rules for identifying the number of significant figures are:
1) All non-zero digits are significant (123 has 3 significant figures).
2) All zeroes between non-zero digits are significant (10203 has 5 significant figures).
3) Leading zeroes are not significant (0.00123 has 3 significant figures).
4) Trailing zeroes in a number containing a decimal point are significant. (150.00 has 5 significant figures)
5) Trailing zeroes in a number not containing a decimal point are not significant (150 has 2 significant figures).
Note: Rule 5 is controversial and some teachers or professors will report that trailing zeroes in a number without a decimal point are significant. It may be helpful to clarify with your teacher or professor regarding rule 5.
Note: Scientific notation has the same rules as above. (1.50 x 102 has 3 significant figures)
Addition and Subtraction
When adding or subtracting numbers, the result must have a certain number of decimal places. The number of decimal places is determined by the original quantity with the least number of decimal places and thus determines the equation’s accuracy.
Example:
1.23 + 4.5678 + 9.0 = 14.8
This is because 9.0 has the least number of decimal places, which is one, and thus our answer can only contain one decimal place.
Multiplication and Division
When multiplying or dividing numbers, the result must have a certain number of significant figures. The number of significant figures is determined by the original quantity with the least number of significant figures.
Example:
2.00 x 4.351 = 8.70
This is because 2.00 has the last number of significant figures, and thus our answer can only contain three significant figures.
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