Significant Figures
Precision & Accuracy in Measurements | Basic Concepts of Chemistry
1. What are Significant Figures?
Significant figures (or sig figs) are the meaningful digits in a measured or calculated quantity. They include all certain digits plus one last digit that is uncertain (estimated).
Precision: Closeness of various measurements to each other.
Accuracy: Agreement of a particular value to the true value.
Accuracy: Agreement of a particular value to the true value.
2. Rules for Counting Significant Figures
| Rule | Example | Sig Figs |
|---|---|---|
| All non-zero digits are significant. | $285$ cm | 3 |
| Zeros between non-zero digits are significant. | $2.005$ | 4 |
| Zeros to the left of the first non-zero digit are NOT significant. | $0.0034$ | 2 |
| Zeros to the right of the decimal point are significant. | $2.500$ | 4 |
| Exact numbers (counting) have infinite sig figs. | 2 balls | $\infty$ |
| Scientific Notation: Power of 10 is NOT significant. | $4.01 \times 10^2$ | 3 |
3. Calculations involving Sig Figs
A. Addition and Subtraction
The result cannot have more digits to the right of the decimal point than any of the original numbers.
Rule: Least Decimal Places
$12.11 + 18.0 + 1.012 = 31.122$
18.0 has 1 decimal place. Result: 31.1
$12.11 + 18.0 + 1.012 = 31.122$
18.0 has 1 decimal place. Result: 31.1
B. Multiplication and Division
The result must be reported with no more significant figures than the measurement with the fewest significant figures.
Rule: Least Significant Figures
$2.5 \times 1.25 = 3.125$
2.5 has 2 sig figs. Result: 3.1
$2.5 \times 1.25 = 3.125$
2.5 has 2 sig figs. Result: 3.1
4. Rules for Rounding Off
- If the digit to be dropped is $< 5$, leave the preceding digit unchanged. ($1.34 \to 1.3$)
- If the digit to be dropped is $> 5$, increase the preceding digit by 1. ($1.36 \to 1.4$)
- If the digit to be dropped is exactly 5:
- If preceding digit is Even, leave it unchanged. ($6.25 \to 6.2$)
- If preceding digit is Odd, increase it by 1. ($6.35 \to 6.4$)
Practice Quiz
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