Significant Figures

1
Significant Figures

• Rounding rules for chemistry

2
What do we need these?

• No such thing as a perfect/exact measurement
• Every number has some amount of uncertainty
• Lab equipment measure to different amount of
  accuracy
• The most accurate piece of lab equipment is the
  Buret
• The least accurate in the beaker
• We round because your answer must reflect the
  least accurate measurement

3
Lets Start

• With the rules for significant figures
• These rules tell us what significant figures are
  and how we determine them for a single number

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Rule 1

• All non-zero digits are significant
• How many significant figures are in the
  following?
• 435 g
• 18 g
• 12.36958 g

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Rule 2

• A zero that falls between two significant digits
  is significant
• Think of book ends
• Example 405 g has 3 sig. figs.
• How many sig. figs. would be in the following?
• 9005 g
• 7000008 g
• 70.8 g

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Rule 3

• Zeros to the right of a significant digit with a
  decimal point are significant
• Example 5.00 g has 3 sig. figs.
• Where as 500 g only has 1 sig. fig.
• And 500. g has 3 sig. figs.

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Lets try some

• How many sig. figs. are in the following
• Look carefully for decimals!
• 4800 g
• 15.200 g
• 12.0 g
• 10. g
• 10 g

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Rule 4

• Zeros to the left of the first significant digit
  are NOT significant
• EVER!!
• Means we are looking at a decimal number
• Example
• 0.151 g
• 0.000405 g
• 0.0000000045 g

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Rule 5

• When looking at scientific notation
• The only part of scientific notation that is
  significant is the M part
• Example
• 5.03 x 1023
• 6.3 x 102

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Now we know what significant figures are

• Lets use them for mathematical operations

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Adding and Subtracting

• The final answer is expressed with the same
  number of DECIMAL PLACES as the measurement with
  the fewest DECIMAL PLACES
• Example
• 89.332 cm
• 1.1 cm
• --------------
• 90.432 cm
• gt 90.4 cm

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Multiplying and Dividing

• The final answer is expressed with the same
  number of SIGNIFICANT FIGURES as the measurement
  with the fewest SIGNIFICANT FIGURES
• Example
• 2.8 cm x 4.5039 cm ?
• 12.61092 cm2
• gt 13 cm2

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Mathematical problems

• Remember Carry as many numbers as possible
  throughout the calculation and only round off the
  final answer

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Summary

• Why do we use significant figures?
• Measurements are used in chemistry to communicate
  information
• We use the measurements taken during the lab and
  experiments to support our findings