BackSignificant Figures and Calculations in Chemistry Measurements
Study Guide - Smart Notes
Tailored notes based on your materials, expanded with key definitions, examples, and context.
Chapter 2: Chemistry and Measurements
Introduction
Accurate measurement and proper reporting of numerical results are fundamental in chemistry. This section covers the rules for determining significant figures, rounding, and performing calculations with measured values, ensuring results reflect the precision of the original data.
Significant Figures in Calculations
Definition and Importance
Significant figures (SFs) are the digits in a measured number that are known with certainty plus one estimated digit.
The number of significant figures in measured numbers determines the number of significant figures in the calculated answer.
Proper use of significant figures ensures that reported results do not imply greater precision than the measurements allow.
Rules for Rounding Off
General Rounding Rules
If the first digit to be dropped is 4 or less, drop it and all following digits.
If the first digit to be dropped is 5 or greater, increase the last retained digit by 1.
Table: Rounding to Significant Figures
Number to Round Off | Three Significant Figures | Two Significant Figures |
|---|---|---|
8.42 (drop 34) | 8.42 | 8.4 |
14.8 (drop 80) | 14.8 | 15 |
3260* (drop 6, increase last retained digit by 1, add 0) (3.26 × 103) | 3260 | 3300* (drop 56, increase last retained digit by 1, add 00) (3.3 × 103) |
*Additional info: The value of a large number is retained by using placeholder zeros to replace dropped digits.
Examples
3.1457 g rounded to three significant figures: 3.15 g
3.1457 g rounded to two significant figures: 3.1 g
Multiplication and Division with Measured Numbers
Rules for Significant Figures
In multiplication or division, the final answer should have the same number of significant figures as the measurement with the fewest significant figures.
Examples
Example 1: (calculator display: 0.875, but answer should be reported as 0.88 cm2 with two significant figures).
Example 2: (calculator display). The answer should be reported as 0.40 (two significant figures).
Adding Significant Zeros
If the calculator display contains fewer significant figures than needed, add zeros to obtain the correct number of significant figures.
Example: (calculator display). To report with two significant figures: 3.0 g.
Addition and Subtraction with Measured Numbers
Rules for Decimal Places
In addition or subtraction, the final answer should have the same number of decimal places as the measurement with the fewest decimal places.
Examples
Example 1 (Addition): (calculator display). The answer should be reported as 6.1 (rounded to the tenths place).
Example 2 (Subtraction): (calculator display). The answer should be reported as 2.1 (rounded to the tenths place).
Summary Table: Significant Figures in Calculations
Operation | Rule for Significant Figures | Example |
|---|---|---|
Multiplication/Division | Answer has the same number of SFs as the measurement with the fewest SFs | (2 SFs) |
Addition/Subtraction | Answer has the same number of decimal places as the measurement with the fewest decimal places | (1 decimal place) |
Practice Problems
Round 3.1457 g to three significant figures: 3.15 g
Round 3.1457 g to two significant figures: 3.1 g
Calculate and report with correct significant figures.
Solution: , (rounded to 2 SFs)
Additional info: These rules are essential for all quantitative work in chemistry, ensuring that results are both accurate and appropriately precise.
