Todays Objectives

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Todays Objectives

• Compare and contrast accuracy and precision
• Identify the purpose of significant digits
• Multiply and divide using significant digit rules

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Precision vs. Accuracy
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Bullseye Represents an Accepted Value
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Bullseye Represents an Accepted Value
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Bullseye Represents an Accepted Value
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Accuracy

• Accuracy is how close something comes to an
  accepted standard.

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Precision

• Precision - how fine the divisions or segments
  are and how repeatable the results.

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• Accurate Correct
• Precision Consistent

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• Ideally an instrument is both accurate and
  precise

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• Precision can add to accuracy if the instrument
  is calibrated correctly.
• Deduct if not ?
• Example Tare (zero) a scale

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Significant Digits
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Significant Digits

• Significant Digits or Sig Digs
• Significant Figures or Sig Figs

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Purpose of Sig. Digs
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Significant Figures Purpose

• Significant digits carry the precision of the
  instrument used.
• Why do them?
• Superfluous precision
• Consistency between people
• Ensures that the precision of the results only
  reflect the precision of the least precise
  measuring tool

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• If a sprinter is measured to have completed a
  100.0 m race in 11.71 seconds, what is his
  average speed?
• Average speed 8.53970965 m/s
• Can we really measure a sprinters speed that
  precisely?

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• Other Options Include
• 8.53970965 m/s
• 8.5397097 m/s
• 8.539710 m/s or 8.53971 (What is the difference?)
• 8.53971 m/s

• 8.5397 m/s
• 8.540 m/s or 8.54 m/s (What is the difference?)
• 8.54 m/s
• 8.5 m/s
• 9 m/s
• Which would you choose?

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• Candle with a mass of 14.143g
• 2.7 hours is the burn time.
• 14.143g/2.7 hrs 5.238148148 g/hr

This number magically became more precise
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• One who makes a squares side 5.1 cm x 5.1 cm is
  not confident that the square is exactly
  26.013496870584764240556 cm2.
• Nor would it be useful to say the square is 30
  cm2
• One has to be careful claiming a greater
  precision than what is justified

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• A good rule of thumb
• No final answer should have any more precision
  attached to it than the LOWEST precision found
  among the numbers being worked.
• Another words you answer should not have more
  digits than the original numbers calculated

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Significant Digit Practice
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Sig Dig Rules

• Nonzero numbers are always significant
• 1.234
• 3876493

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Sig Dig Rules

• All final zeros after the decimal point are
  significant
• 1.000000, 345.600

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Sig Dig Rules

• Zeros between two other significant digits are
  always significant.
• 1.001, 234.01, 3.404040

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Sig Dig Rules

• Zeros used solely as placeholders are not
  significant.
• 0.0002, 0.0231, 0.003040

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Practice Time
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How Many Sig Digs?

• 100
• 10.98
• 0.0034
• 0.0480

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How Many Sig Digs?

• 6.0490
• 303000
• 4.030
• .00000010

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Calculating With Sig Digs

• Scientific Notation
• Multiplying and Dividing Sig Digs

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Density of Paper Clips

• Page 52

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Thickness of Aluminum Foil

• Page 52

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Salt Water Aquarium

• Page 52

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Tea Bags

• Page 52

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Deionized Water

• Page 52