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Significant Figures (sig figs)
Definition:
Significant figures or sig figs are the digits of value which carry meaning towards the resolution of the measurement. They include all the non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal.
Rules for Identifying Significant Figures
Non-zero digits:
All non-zero digits (1-9) are significant
Zeros between non-zero digits:
Zeros between significant digits are significant
Leading zeros:
Zeros to the left of the first non-zero digit are not significant
Trailing zeros in a whole number:
Zeros at the end of a whole number without a decimal point are not considered significant unless specified
Trailing zeros in a decimal:
Zeros to the right of the decimal point and after a non-zero digit are significant
Significant Figures Examples
| Number | Number of Significant Figure |
|---|---|
| 3000 | one significant figure |
| 0.003 | one significant figure |
| 87 | two significant figures |
| 9500 | two significant figures |
| 5.760 | three significant figures |
| 9723 | four significant figures |
| 237810 | five significant figures |
Calculations with Significant Figures:
Any calculation (addition, subtraction, multiplication, division) should have the same number of significan’t figures as the measurement with the least amount of significant figures.
Calculations with Significant Figures and Rounding Examples:
- Addition: $\sqrt{17}+8 = 12$
- Subtraction: 0.034 - 0.08 = -0.05
- Multiplication: 2.3 * 400 = 920
- Division: $\frac{5800}{4} = 1000$
Rounding Rules:
- If the first digit to be dropped is less than 5 then the last retained digit stays the same
- If the first digit dropped is greater than or equal to 5 round up the last retained digit
Rounding Significant Figures Example:
Importance of Significant Figures:
- They show the precision of measurements and calculations in scientific work
- When the correct number of significant figures is used it ensures clarity and accuracy in data presentation
Tips When Using Significant Figures:
- Always identify the number of significant figures before performing any calculations
- Use scientific notation to clearly specify significant figure in large or small numbers
- Double check your rounding in the calculation’s answer to ensure accuracy