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Significant Figures and Rounding. Counting Sig. Figs. P acific a.k.a.: P resent Start with first non-zero, go in  direction. A tlantic a.k.a.: A bsent Start with first non-zero, go in  direction. Steps to Count # of Sig. Figs. See if decimal is present or not.

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counting sig figs
Counting Sig. Figs.

Pacific

a.k.a.: Present

Start with first non-zero, go in direction

Atlantic

a.k.a.: Absent

Start with first non-zero, go in  direction

  • Steps to Count # of Sig. Figs.
  • See if decimal is present or not.
  • Go from correct direction.
  • Start counting at 1st Non-Zero #
  • Keep counting until you run out of #s
examples
Examples
  • 300,150
    • Decimal point absent – 5 sig figs
  • 300.0
    • Decimal point present – 4 sig figs
  • 300
    • Decimal point absent – 1 sig fig
  • 0.0000015
    • Decimal point present – 2 sig figs
  • 631.10
    • Decimal point present – 5 sig figs
rounding sig figs
Rounding Sig. Figs.
  • Always start from the LEFT
  • Start counting at the 1st non-zero #
  • Count to the correct # of Sig. Figs.
  • Round that #
    • If that # is a 0 before the ones position, then turn to sci. not. and then round.
  • For every # after the rounded position
    • If before decimal, turn to zero
    • If after decimal, drop
example round 0 065930 to 2 s f
Example – Round 0.065930 to 2 S.F.
  • Always start from the LEFT
    • 0.065930
  • Start counting at the 1st non-zero #
    • 0.065930
  • Count to the correct # of Sig. Figs.
    • 0.065930
  • Round that #
    • 0.065930

Final Answer: 0.066

example round 0 065930 to 3 s f
Example – Round 0.065930 to 3S.F.
  • Always start from the LEFT
    • 0.065930
  • Start counting at the 1st non-zero #
    • 0.065930
  • Count to the correct # of Sig. Figs.
    • 0.065930
  • Round that #
    • 0.065930

Final Answer: 0.0659

slide7

Examples:

  • 135.35 (4 S.F.)
  • 135.35 (2 S.F.)
  • 1.506 x 104 (3 S.F.)
  • 5.80354 (3 S.F.)
  • 100 (2 S.F.)
determining the number of sig figs in calculations
Determining the Number of Sig Figs in Calculations
  • Find out the # of sig. figs. for all numbers
  • Round to the lowest # of S. F.

Ex: 3.8 x 4.50 = (Round to 2 S.F.)

determining the number of sig figs in calculations1
Determining the Number of Sig Figs in Calculations
  • Round to the lowest place holding # that all of them have in common

Ex:

+ 12.0

+ 134.354

147.664 = 147.7