Significant Digits and Scientific Notation

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Significant Digitsand Scientific Notation
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Accuracy vs Precision

• An accurate measurement is close to the true
  value.
• Precision gives an idea of the reliability of a
  measurement
• Precision is a measure of the agreement among a
  series of measurements.

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Significant Digits

• Significant digits are the digits in a
  measurement that are known to be precise

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Which digits are significant?

• Significant

• Not Significant

• Non-zero digits
• Zeros in the middle
• Zeros at the end
• As long as there is a decimal point somewhere in
  the number
• Exact numbers and integers have infinite
  significant figures

• Leading zeros
• x10n in scientific notation

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• 87032
• 74000
• 8.900
• 0.000342
• 0.002190

• 1000
• 1000.
• 01000
• 1 x 103
• 1.0 x 103

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Sig. Figs. in Lab

• All of the digits in the readout a digital
  apparatus are significant and should be written
  down.
• Don't round off or drop zeros.
• Your calculator is not included.

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Analog Scales

• The digit not read from the written scale is the
  estimated digit
• Example 82.5mL estimated digit 5

• Analog scales are read to one tenth of the
  smallest graduation present.
• Example Scale is graduated every 1 mL, so
  reading should be to the nearest 0.1 mL.
• Don't round off or drop zeros.
• Example 29.0mL

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Calculations with Sig. Figs.

• Calculations involving measurements
• Significant figures depends on the sig figs of
  the measurements
• The weakest link principle
• Least number of sig figs is limiting
• One rule for addition and subtraction different
  rule for multiplication and division.

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Addition and Subtraction

• RULE When adding and subtracting, the result
  should have the same number of decimal places as
  the least precise number added.
• Example 26.098 3.92
• 534.1-265.36

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Multiplication and Division

• RULE When multiplying or dividing, the result
  should have the same number of significant
  figures as the number with least significant
  figures.
• Example 3.28 x 2.1
• 87.008 7.20

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Longer Calculations

• In a calculation with several steps, the final
  result must be rounded off to the correct sig.
  figs.
• Rounding off intermediate results may cause
  cumulative round-off errors.
• Dont round until the end.
• (2.34 x 1.3) 23.18
• 8.35 2.73 (5.31 3.001)

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Scientific Notation

• Use scientific notation to eliminate place
  holding zeros.
• Move the decimal so that only 1 digit remains in
  front of the decimal. Then change the exponent
  accordingly.
• If you move the decimal to the right the exponent
  is negative.
• If you move the decimal to the left the exponent
  is positive
• Round to the correct number of sig figs
• 43200000
• 0.00264

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• When taking a number out of scientific notation
  move the decimal in the opposite direction and
  fill the empty spaces with 0s
• If the exponent is negative move the decimal
  point to the left
• If the exponent is positive move the decimal
  point to the right
• 3.46 x 10-5
• 8.138 x 108