Significant Figures

Definitions:

• Precision: How easy it is to reproduce a measurement
• Accuracy: How close the measurement is to the actual value
• Significant Figures: Measured or meaningful digits. The higher number of significant figures = more precise number

Accuracy Vs Precision

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Significant Figures

Part I:

• The last number is always uncertain as it can easily be a digit higher or lower
• Significant digits include all certain digits (known digits) plus one uncertain
• Eg: 3.87329 
• Certain/Uncertain
• 6 Sig Figs

Part II:

• Leading Zero's are NEVER counted
• Zero's at end, if they are after a decimal ARE counted. If no decimal, they ARE NOT.
• Eg:
• 0.00000006 = 1 SF
• 12.000 = 5 SF
• 12000 = 2 SF

Part III: Exact Numbers

• Some amounts are defined to an exact point - no rounding needed
• Other's have an infinite number of significant digits
• Eg:
• If you have two light bulbs, you have two whole light bulbs, not 1.899999934583 light bulbs

Part IV: The Rules of Rounding

• Usually rounded the same way as in math
• EXCEPTIONS
• if the digit is equal to 5, and there are more non-zero digits after it, round up.
• If the digit is equal to 5 and there are NO more non-zero digits after it, make the last digit even
• Eg:
• 9.86356 to 3 SF = 9.86
• 4.87625 to 4 SF = 4.8763
• 12.065 to 2 SF = 12.06
• 12.075 to 2 SF = 12.08

Part V: Connections with Math

• When Adding or Subtracting, round to the fewest number of decimals

• When Multiplying or dividing, round to the fewest number of significant digits.
• Cannot have any more than the least number of significant digits
• DO NOT ROUND UNTIL CALCULATION IS COMPLETE!!!

PRACTICE QUIZ

Significant Figures and Rounding Quiz