BackSignificant Figures (Sig Figs) in Measurement and Calculations
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Significant Figures (Sig Figs)
Introduction to Significant Figures
Significant figures are crucial in chemistry for expressing the precision of measurements and calculations. They indicate which digits in a number are meaningful and reflect the accuracy of the measurement instrument.
Definition: Significant figures are the digits in a measurement that are known with certainty plus one digit that is estimated.
Purpose: To communicate the precision of measured quantities and ensure proper reporting in scientific work.
Rules for Identifying Significant Figures
There are specific rules to determine which digits in a number are significant:
Nonzero digits: Always significant. Example: 123.45 has 5 significant figures.
Leading zeros: Never significant (they only indicate the position of the decimal point). Example: 0.0025 has 2 significant figures.
Captive (embedded) zeros: Always significant. Example: 1002 has 4 significant figures.
Trailing zeros: Significant only if there is a decimal point. Example: 100.0 has 4 significant figures; 100 has 1 significant figure.
Counting Significant Figures
Exact numbers: Have an infinite number of significant figures (e.g., counting objects, defined quantities).
Scientific notation: All digits in the coefficient are significant. Example: has 3 significant figures.
Significant Figures in Calculations
Multiplication and Division
For multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures.
Rule: The answer must match the least number of significant figures in the input values.
Example: (but should be reported as since 2.5 has 2 sig figs).
Addition and Subtraction
For addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places.
Rule: The answer must match the least number of decimal places in the input values.
Example: (but should be reported as since 18.0 has 1 decimal place).
Rounding Rules
If the digit to be dropped is less than 5, leave the last retained digit unchanged.
If the digit to be dropped is 5 or greater, increase the last retained digit by one.
Example: Rounding 2.348 to 2 significant figures gives 2.3; rounding 2.35 to 2 significant figures gives 2.4.
Examples and Applications
Example 1: How many significant figures in 0.00450? Answer: 3 significant figures (4, 5, and the trailing zero).
Example 2: (should be reported as $23$ since 7.0 has 2 sig figs).
Example 3: (should be reported as ).
Summary Table: Significant Figure Rules
Rule | Example | Sig Figs |
|---|---|---|
Nonzero digits | 123.45 | 5 |
Leading zeros | 0.0025 | 2 |
Captive zeros | 1002 | 4 |
Trailing zeros (with decimal) | 100.0 | 4 |
Trailing zeros (no decimal) | 100 | 1 |
Scientific notation | 3 |
Additional info:
Significant figures are foundational for reporting measurements in chemistry and are covered in Ch.1 - Matter, Measurement & Problem Solving.
Proper use of significant figures ensures scientific accuracy and reliability in experimental results.
