Significant Figures---Purpose is to show precision; the last digit is estimated

1
Significant Figures---Purpose is to show
precision the last digit is estimated

• Sig Fig Rules
• Rounding Rules
• Addition/Subtraction with Sig Figs
• Multiplication/Division with Sig Figs

2
Sig Fig Rules (p. 39 Blue, p. 66 Orange)

• 1. Non-zero numbers are always significant
  72.3 (3) 24.7 (3) 714 (3)
• 2. Zeroes between non-zero numbers are always
  significant 60.5 (3) 7003 (4) 40.79 (4)
  1.503 (4)
• 3. All final zeros to the right of the decimal
  place are significant 6.20 (3) 43.00 (4) 1.010
  (4) 9.000 (4)

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Sig Fig Rules (p. 39 Blue, p. 66 Orange)

• 4. Zeros that act as placeholders are not
  significant (2 ways!!!!)
• 0.0253 (cross out the front two zeros so you have
  3 sig figs)
• 4320 (cross out the last zero since no decimal
  point) so 3 sig figs
• IF DECIMAL POINT, THEN 4320. WOULD HAVE 4 SIG
  FIGS (to indicate that is a precise, measured
  value)
• Additional point Write Rule 4 instances in
  scientific notation to eliminate placeholder
  zeros (0.0071 goes to 7.1 10-3 300. goes to
  3.00 102)---review scientific notation!!

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Sig Fig Rules (p. 39 Blue, p. 66 Orange)

• 5. Defined constants and counting numbers have
  an infinite number of sig figs---do NOT consider
  FOR SIG FIGS
• (24 hours/day 60 seconds/minute 365 days/year)

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Rounding Rules---Common Sense (p. 40 Blue)

• Only look at Rules 1 and 2
• 1. If the digit to the immediate right of the
  last sig fig is less than 5, do not change the
  last sig fig (to round 2.532 to 3 sig figs means
  it becomes 2.53 (the 2 was less than 5 so the 3
  was not changed)
• 2. If the digit to the right of the last sig fig
  is 5 or greater, round the last sig fig up (2.536
  goes to 2.54 to get 3 sig figs)

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Addition/Subtraction Sig Fig Rules(p. 41 blue,
p. 70 orange)

• Same rule for addition or subtraction
• The answer must show the LEAST NUMBER OF DECIMAL
  PLACES from the problem
• Line up the decimal points so you dont make a
  mistake
• 12.52
• 349.0 (LOWEST DECIMAL PLACE)
• 8.24
• -----------
• 369.76 (not the answer yet)
• 369.8---Answer (6 was greater than 5 so it made
  the 7 increase for rounding)

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Multiplication/Division Sig Figs

• Same Rule for Multiplication or Division
• Answer must show the LEAST NUMBER OF SIG FIGS
  FROM THE PROBLEM (DO NOT LOOK AT DECIMAL
  PLACES!!!)
• 1.23 2.0 2.46 (NOT ANSWER) (2.0 IS THE LOWEST
  SIG FIG DO NOT EVEN CONSIDER DECIMAL PLACES)
• Answer is 2.5 (2 sig figs like 2.0 has 2 sig
  figs!!)
• Had to round the 4 because a 6 was to the right

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Practice Problems From Book

• We went over book examples and problems for sig
  figs, rounding, addition/subtraction,
  multiplication/division from each book---I hope
  you took notes!!!!
• Blue p. 39-42 practice problems 31, 32, 33, 34,
  35, 36, 37, 38
• Orange p. 66-72 practice problems 1, 2, 3, 4, 5,
  6 (word problem), 7, 8

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Quiz Coming Soon!

• Tuesdays in-class assignment will be very
  similar to the quiz
• Practice makes perfect
• Hopefully these slides help to clarify the topics
  so you can study at home with the book, the
  problems, your notes, and the assignment