Significant Figures or Digits

1
Significant Figuresor Digits

• Take notes, this is important!

2
What are Significant Digits?

• The Important Numbers
• Representatives of the precision and accuracy of
  measurements.
• Absolutely Necessary!

3
Why Do We Have Significant Digits?

• They limit the number of decimal places
• They give our calculations relevance
• They make students crazy

4
Identifying Significant digits

• A SigFig is
• All nonzero numbers
• Leading zero non significant
• Captive zeros (zeros in between nonzero numbers)
• Trailing zeros when a decimal is present

5
Identifying Significant Digits

• A SigFig is not
• Leading zeros
• Trailing zeros when there is no decimal

6
Are Zeros Significant?

• Trailing - If a decimal is present
• Leading Never
• Captive Always

7
Identifying Significant Digits

• 12,345.67 All are SigFigs
• 1,234,000 4 SigFigs
• 0.000123 3 SigFigs
• 1,020,304 All are SigFigs
• 0.0120340 6 SigFigs
• 1.230 x 10-6 4 SigFigs
• 0.0001000 4 SigFigs

8
Using Significant Digits

• Adding and Subtracting - The final calculated
  answer should have the same of decimal places
  as the measurement that is the least accurate
  (least of decimal places).
• Multiplying and Dividing- The final calculated
  answer should have the same of SigFigs as
  measurement with least of Sig Figs.

9
Rounding Rules

• If a digit is to be cut off, and it is less than
  5, the before the cut remains the same.
• If a digit is to be cut off, and it is greater
  than or equal to 5, then the before the cutoff
  is increased by 1.
• Always wait to round s until the last
  calculation is completed.