Significant Figures: Concepts, Rules, and Calculations

Significant Figures in Chemistry

Introduction to Significant Figures

Significant figures (often abbreviated as "sig figs") are the digits in a measurement that are known with certainty plus one digit that is estimated. Understanding and applying the rules of significant figures is essential in chemistry to ensure that calculated results reflect the precision of the measurements used.

• Significant figures communicate the reliability and precision of measured values.

• They are crucial when performing mathematical operations with measured data, as results cannot be more precise than the least precise measurement.

Rules for Identifying Significant Figures

General Rules

• All nonzero digits are always significant.

• Zeros may or may not be significant, depending on their position in the number.

Rules for Zeros

• Leading zeros: Zeros that precede all nonzero digits are not significant. Example: 0.563 g has 3 significant figures.

• Captive zeros: Zeros between nonzero digits are always significant. Example: 5008 km has 4 significant figures.

• Trailing zeros: Zeros at the end of a number are significant only if the number contains a decimal point. Example: 500.0 mL (4 significant figures); 500 mL (1 significant figure).

Examples of Counting Significant Figures

• 0.010020 m → 5 significant figures

• 38.2123 → 6 significant figures

• 0.0045 → 2 significant figures

Why Are Significant Figures Important?

• They reflect the precision of the measurement scale used.

• They ensure that calculated results do not imply greater precision than the measurements allow.

• They are essential for proper reporting and interpretation of scientific data.

Significant Figures in Calculations

Multiplication and Division

When multiplying or dividing measured values, the result should have the same number of significant figures as the measurement with the fewest significant figures.

1. Count the significant figures in each number.

2. Perform the calculation.

3. Round the result to the correct number of significant figures.

Example:

• 770 × 6.72 = 5174.4 (calculator result)

• 770 has 2 significant figures; 6.72 has 3 significant figures.

• Final answer: 5200 (rounded to 2 significant figures)

Addition and Subtraction

When adding or subtracting measured values, the result should have the same number of decimal places as the measurement with the fewest decimal places.

1. Count the number of digits after the decimal point for each number.

2. Perform the calculation.

3. Round the result to the correct number of decimal places.

Example:

• 1.9 + 38.2123 + 33.5 = 73.6123 (calculator result)

• 1.9 (1 decimal place), 38.2123 (4 decimal places), 33.5 (1 decimal place)

• Final answer: 73.6 (rounded to 1 decimal place)

Practice: Determining Significant Figures

Practice problems help reinforce the rules for counting significant figures. For each measurement, determine the number of significant figures:

Measurement	Significant Figures
0.0045	2
38.2123	6
0.010020	5
5008	4
500.0	4
500	1
0.563	3
0.010	2
0.100	3
0.00100	3
0.0001	1
0.00010	2

Summary Table: Rules for Significant Figures

Type of Digit	Rule	Example	Sig Figs
Nonzero digits	Always significant	123	3
Leading zeros	Never significant	0.045	2
Captive zeros	Always significant	1002	4
Trailing zeros (with decimal)	Significant	2.300	4
Trailing zeros (no decimal)	Not significant	1500	2

Key Equations

• Multiplication/Division: Result has the same number of significant figures as the measurement with the fewest significant figures.

• Addition/Subtraction: Result has the same number of decimal places as the measurement with the fewest decimal places.

Additional info: Mastery of significant figures is foundational for all subsequent quantitative work in chemistry, including stoichiometry, solution preparation, and data analysis.