1. All non-zero digits (1-9) are to be counted as significant.
2. Zeros that have any non-zero digits anywhere to the left of them are considered
significant zeros. All other zeros are not considered significant digits.
Numbers such as 1,000,000 without an indicated decimal point have an inherent ambiguity about the number of significant digits. Such numbers should be written in exponential notation to clarify the ambiguity. The above rules are then applied to the mantissa.
Examples:
1 x106 has 1 significant digit; 1.00 x106 has 3 significant digits ; 1.0000 x106 has 5 significant digits.
Exercises:
Determine the number of significant digits in each of these numbers:
1. 6.751 2. 100.123 3. 0.001 4. 2.500 x 10-2 5. 2.5 x 10-2
The product (or quotient) should be reported as having as many significant digits as the number used the computation which has the least number of significant digits.
Example: 0.00280 X 100.10 = .28028
This product should be expressed with three significant digits ( .00280 has 3 and 100.10 has 5 significant digits). Hence the answer should be reported as .280
The sum (or difference) can be no more precise (in terms of number of digits to the right of the decimal place) than the least precise number used in the computation.
Examples: 4160.45 + 5.123 = 4165.573 should be reported as 4165.57
1.4523 + .012 = 1.4643 should be reported as 1.464
Exercises: Determine the answer to the appropriate number of significant digits:
1. 3.250 + 0.32145 2. 3.250 * 0.32145
3. 113.250 + 2.321 4. 113.250 * 2.321
Rule for Intermediate Calculations: Keep at least one extra digit in intermediate answers than will be reported in your final answer. (Or, if on calculator, do not round until you get your final answer!) Example: If a final answer requires three significant digits, then carry at least four significant digits in calculations.