Understanding Significant Figures
Significant figures (often called "sig figs") are the digits in a number that express precision rather than a mere placeholder. In chemistry, physics, and engineering, reporting measurements with the correct number of significant figures is just as important as getting the math right.
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The Golden Rules of Significant Figures
Determining which digits are significant can be confusing because zeros can act either as measured values or mere decimal markers. Here are the foundational rules:
1. Non-Zero Digits & Captive Zeros
All non-zero digits (1 through 9) are always significant. Furthermore, zeros sandwiched between non-zero digits (captive zeros) are also always significant.
Example: 405 has 3 significant figures.
2. Leading Zeros
Zeros placed before the first non-zero digit (leading zeros) are never significant. They exist solely to position the decimal point.
Example: 0.0052 has 2 significant figures (5 and 2).
3. Trailing Zeros
Trailing zeros (zeros at the right end of a number) are significant only if the number contains a decimal point. If there is no decimal point, trailing zeros are considered ambiguous placeholders.
• 450.0 → 4 sig figs (decimal present)
• 4500 → 2 sig figs (ambiguous without scientific notation)
Frequently Asked Questions (FAQs)
What are significant figures?
Significant figures are the digits in any number that carry actual meaning contributing to its measured precision. This includes all non-zero digits, captive zeros, and trailing zeros when a decimal point is explicitly shown.
Are leading zeros significant?
No, leading zeros (zeros placed before the first non-zero digit, like in 0.0045) are never significant. They serve only to locate the decimal point in small quantities.
How do you handle sig figs in multiplication and division?
In multiplication and division, your final calculated result must be rounded to have the exact same number of significant figures as the measured value with the fewest significant figures in your equation.
How do you handle sig figs in addition and subtraction?
Unlike multiplication and division, addition and subtraction depend on decimal places rather than total sig figs. Your final result must be rounded to match the fewest decimal places present in any of the contributing measurements.