Significant Figures

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Topic Summary & Highlights
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Core Concept

Significant figures, also known as significant digits or sig figs, provide a way to convey the reliability and limitations of measurements and calculations. They indicate the precision of a measurement and convey the level of certainty or uncertainty associated with it. 

Practice Tips

  • Significant figures reflect the precision of a measurement or calculation and must align with the least precise value used.

  • Ignoring Rules for Zeros: Misidentifying leading, captive, or trailing zeros.

  • Forgetting the Input Precision: Failing to adjust significant figures in calculations to match the least precise measurement.

  • Mixing Up Decimal Places and Significant Figures: Decimal places matter only in addition/subtraction; significant figures are the focus in multiplication/division.

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Counting Significant Figures

Rule Examples
If there is a decimal point present, start at the LEFT and count, beginning with the first non-zero digit. 340. → 3 significant figures
30400. → 5 significant figures
0.34955 → 5 significant figures
0.00500 → 3 significant figures
If there is NOT a decimal point present, start at the RIGHT and count, beginning with the first non-zero digit. 340 → 2 significant figures
30400 → 3 significant figures
34955 → 5 significant figures
Counting numbers, conversions, and accepted values have unlimited (infinite) significant figures. Examples: 12 apples, 1 inch = 2.54 cm (exact conversion)

Rules for Significant Figures in Calculations

Addition and Subtraction:

  • The result should have the same number of decimal places as the measurement with the fewest decimal places.

    • Example: 12.34+0.6=12.94 (round to 1 decimal place: 12.9)12.34 + 0.6 = 12.94 \, \text{(round to 1 decimal place: } 12.9\text{)}12.34+0.6=12.94(round to 1 decimal place: 12.9)

Multiplication and Division:

  • The result should have the same number of significant figures as the measurement with the fewest significant figures.

    • Example: 4.56×1.4=6.384 (round to 2 significant figures: 6.4)4.56 \times 1.4 = 6.384 \, \text{(round to 2 significant figures: } 6.4\text{)}4.56×1.4=6.384(round to 2 significant figures: 6.4)

Logarithms:

  • The result should have the same number of decimal places as the number of significant figures in the input value.

    • Example: log⁡(4.56)=0.659 (input has 3 sig figs, so the result has 3 decimal places).\log(4.56) = 0.659 \, \text{(input has 3 sig figs, so the result has 3 decimal places).}log(4.56)=0.659(input has 3 sig figs, so the result has 3 decimal places).

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