Significant Digits or Significant Figures

1
Significant Digitsor Significant Figures
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WHY???

• The number of significant figures in a
  measurement is equal to the number of digits that
  are known with some degree of confidence
• (i.e. our good friends ACCURACY and PRECISION)

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What is significant??

• In a measurement, such as 3.25, the significant
  digits include the number of digits that are
  known with some degree of confidence (3 and 2)
  plus the last digit (5), which is an estimate or
  approximation.

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Rules for counting Sig Figs

• Zeros within a number are always significant
• Both 4308 and 40.05 contain four significant
  figures
• Zeros that do nothing but set the decimal point
  (place holders) are not significant
• 470,000 and 0.000047 have two significant figures
  
• Trailing zeros that aren't needed to hold the
  decimal point are significant
• 4.00 and 0.00400 have three significant figures

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Practice

• 12.760
• 0.00034
• 9.0034
• 0.0901
• 3.8 x 107

• 1.096 x 10-3
• 987 600
• 54 004
• -43.803
• 0.210

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Rules for rounding off

• Imagine that you want to have 2 significant
  digits.
• If the digit after is smaller than 5 (lt5), dont
  change the digit.
• Ex 12. 4 ? 12
• If the digit after is gt 5, round up.
• Ex 12. 6 ? 13
• If the digit after is 5
• If the digit that you are rounding is even, round
  down.
• Ex 12,5 ? 12
• If the digit that you are rounding is odd, round
  up
• Ex 17.5 ? 18

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Practice

• Round off to have 3 significant figures.
• 1.854
• 96.019
• 974 501
• 273.51
• 930.8
• 381.5
• 0.004 745

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What if theyre not all the same??

• How do you calculate the significant figures in
  the answer to an equation where the components
  have different sig figs?
• 150.0
• 0.507
• 0.005580
• x 67

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3
Now what??
4
2
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IMPORTANT

• When combining measurements with different
  degrees of accuracy and precision, the accuracy
  of the final answer can be no greater than the
  least accurate measurement.

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Addition and Subtraction with Significant Figures

• A simple rule for addition and subtraction
• When measurements are added or subtracted, the
  answer can contain no more decimal places than
  the least accurate measurement.

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Practice

• 14m/s 11.8m/s
• 0.370m 0.4876m
• 45.23s 3.8s
• 130.0m 5.43m
• 58.035cm 4.72cm

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Multiplication and Division With Significant
Figures

• A simple rule for multiplication and division
• When measurements are multiplied or divided, the
  answer can contain no more significant figures
  than the least accurate measurement.

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Exceptions!!

• Counting numbers are not used to calculate the
  number of significant digits
• Example If 124.79 grams of candy are to be
  divided among 4 children, how many grams would
  each child receive?
• The number 4 is a counting number.
• The answer would be given with 5 significant
  digits

124.79
4
4
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Exceptions!!

• Constant values are not used to calculate the
  number of significant digits
• Example How many minutes are there in 2.75
  hours?
• The constant value used in this calculation is
  60 minutes/hour, but the number of significant
  digits in 60 is not counted.
• The answer would be given with 3 significant
  digits

2.75