Significant Figures

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Significant Figures

• But their friends call them sig figs

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• Only those who have the patience to do simple
  things perfectly will acquire the skill to do
  difficult things easily.
• Johann von Shiller

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Measurements

• Numbers in science class are measurements, and
  have a meaning.
• In the measurement, .0045 cm, the zeros are just
  place holders for the measurement digits of 4 and
  5.
• We could rewrite this as 4.5x10-3 without losing
  any accuracy, so these zeros dont matter as much
  as the 4 and five.

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Sig Figs

• Numbers that are important in a measurement are
  called significant figures.
• There are four simple rules we can follow to
  determine which numbers are sig figs in a
  measurement.

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Rule 1

• Every nonzero number is a sig fig.
• 2300 has two sig figs, the 2 and the 3
• 12.43 has four sig figs
• How about 724000?
• Three sig figs!

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Rule 2

• Zeroes trapped are sig figs.
• 203 has three sig figs
• The two and three because of rule 1
• The zero is trapped, so its a sig fig
• 1.024 has four sig figs
• How many sig figs are in 609,000?
• Three!

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Rule 3

• Zeros on the left are not sig figs.
• .0045 has two sig figs
• .0203 has three sig figs
• How many sig figs are in .004903?
• Four sig figs!

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Rule 4

• Final zeros to the right of the decimal are sig
  figs.
• .04900 has four sig figs
• 1.0030 has five sig figs
• How many sig figs are in 3.00?
• 3 sig figs!

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How many sig figs are in each measurement?

• 7.50
• 4.304
• .0070
• 4.200 x 102

• 3
• 4
• 2
• 4
• (the 10 factor doesnt count)

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Why does this matter?

• When we use measurements to do math, we often end
  up with more digits than we started with.
• Ex.
• Find the area of a triangle with a base of .3 cm
  and height of 1.5 cm.
• Area .225 cm2
• Problem, we have an answer that is accurate to
  the thousandths place, but the measurements were
  only accurate to the tenth.

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Old Man! Im Confused!

• I will show you a trick.
• Remember tricks are useful, but dont confuse
  them with understanding

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If there is a decimal

• If there is a decimal, we bring an arrow from the
  left
• .0004560
• The arrow goes through any zeros.
• It stops when it hits a number.
• Everything left is a sig fig

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If there is no decimal

• If there is no decimal, we bring an arrow from
  the right
• 780000
• The arrow goes through any zeros.
• It stops when it hits a number.
• Everything left is a sig fig

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Assignment

• Page 51
• 83 and 84
• Add this to previous book work
• Need help? More info on sig figs can be found on
  pages 38-39, including some samples.