SIG FIGS

1
SIG FIGS

• SIGNIFICANT FIGURES

2
SIG FIGS

• THERE ARE TWO TYPES OF NUMBERS IN SCIENCE...

3
SIG FIGS

• THOSE FROM COUNTING
• /DEFINITION,
• THOSE
• MEASURED

4
SIG FIGS

• COUNTED/ DEFINED IE
• 32 CHAIRS IN
• THE
• CLASSROOM
• 60 MIN/HR

5
SIG FIGS

• COUNTED/ DEFINED IE
• ARE NOT SUBJECT TO ERROR

6
SIG FIGS

• MEASURED
• NUMBERS
• ALWAYS
• HAVE SOME
• UNCERTAINTY

7
SIG FIGS

• UNCERTAINTY
• IS DUE TO
• PRECISION OF
• THE INSTRU-
• MENT TO THE
• USERS SKILL

8
SIG FIGS

• SOME USERS
• ARE MORE
• SKILLED,
• CAREFUL,
• RESTED, ETC

9
SIG FIGS

• OTHERS
• HAVE LESS
• PRACTICE,
• ARE TIRED,
• ARE ILL, ETC.

10
SIG FIGS

• SLOPPINESS,
• HOWEVER, IS NO EXCUSE FOR HUMAN ERROR

11
SIG FIGS

• THE
• PRECISION
• OF THE IN-
• TRUMENT AFFECTS...

12
SIG FIGS

• THE NUMBERS
• REPORTED BY MEASURE- MENT

13
SIG FIGS

• METERSTICK A
• IS MARKED
• IN CM
• INCREMENTS

A
14
SIG FIGS

• THE DESK IS BETWEEN
• 82 CM
• 83 CM
• WIDE

A
15
SIG FIGS

• THE DESK CAN BE ESTIMATED TO BE
• 82.2 CM WIDE

A
16
SIG FIGS

• METERSTICK
• B
• IS MARKED IN MM

B
17
SIG FIGS

• IT SHOWS THE DESK
• IS BETWEEN
• 82.2 82.3 CM
• WIDE

B
18
SIG FIGS

• WITH THIS
• METERSTICK,
• THE DESK IS
• ESTIMATED
• TO BE 82.25 CM

B
19
SIG FIGS

• MEASURE-
• MENTS CONVEY
• MAGNITUDE
• AND

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SIG FIGS

• PRECISION
• OF THE
• INSTRU- MENT

21
SIG FIGS

• PRECISION IS INDICATED BY THE SIG FIG REPORTED

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SIG FIGS

• A SIGNIFICANT FIGURE
• IN ANY MEASUREMENT
• IS KNOWN WITH
• CERTAINTY PLUS ONE
• DIGIT THAT IS ESTIMATED

?
23
SIG FIGS

• THE RIGHT
• MOST DIGIT
• IS ALWAYS
• ESTIMATED

24
SIG FIGS

• ONLY ONE ESTIMATED
• DIGIT IS EVER RECORDED

25
SIG FIGS

• SO, USING OUR EXAMPLE, A VALUE OF 82.253 WOULD
  NEVER BE RECORDED

26
SIG FIGS

• HOW IS ONE TO READ SIG FIGS ???

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SIG FIGS- RULE 1

• ALL DIGITS 1-9,
• INCLUSIVE,
• ARE SIG FIGS

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SIG FIGS- RULE 1

• IE
• 129
• HAS 3 SIG FIGS

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SIG FIGS- RULE 2

• ZEROS BETWEEN
• SIGNIFICANT DIGITS ARE ALWAYS SIGNIFICANT

30
SIG FIGS- RULE 2

• IE
• 5,007
• HAS 4 SIG FIGS

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SIG FIGS- RULE 3

• TRAILING ZEROS IN A NUMBER ARE SIGNIFICANT ONLY
  IF THE NUMBER CONTAINS A DECIMAL POINT

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SIG FIGS- RULE 3

• IE
• 100.0 HAS 4 SIG FIGS
• BUT
• 1OO HAS ONLY 1 S.F.

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SIG FIGS- RULE 4

• ZEROS IN THE BEGIN-
• -ING OF A NUMBER
• WHOSE ONLY FUNC-
• TION IS TO PLACE THE
• DECIMAL POINT ARE
• NOT SIGNIFICANT

34
SIG FIGS- RULE 4

• IE
• 0.0025
• HAS 2 SIG FIGS

35
SIG FIGS- RULE 5

• ZEROS FOLLOWING A DECIMAL SIG FIG
• ARE ALWAYS SIGNIFICANT

36
SIG FIGS- RULE 5

• IE
• 0.000470
• HAS 3 SIG FIGS
• BUT

37
SIG FIGS- RULE 5

• IE
• 0.47000
• HAS 5 SIG FIGS

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SIG FIGS

• IS THERE
• ANY HELP ON THE WAY?

39
SIG FIGS

• OUR MEASURE-MENTS ARE USUALLY TO THE TENTH OR
  HUNDRETH PLACE

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SIG FIGS

• AND
• CALCULATE TO THE NEAREST HUNDREDTH OF A UNIT

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SIG FIGS

• THAT MEANS
• LOOK AT THE THIRD DIGIT BEHIND THE DECIMAL

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SIG FIGS

• IF THAT DIGIT
• IS 4 OR LESS, LET
• THE 2ND DIGIT
• ALONE AND DROP
• THE ONES
• BEHIND IT

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SIG FIGS

• IF THAT DIGIT
• IS 5 OR MORE, IN-
• CREASE THE 2ND
• DIGIT BY ONE
• AND DROP THE
• ONES BEHIND IT.

44
SIG FIGS

• IE
• ROUND 12.90090
• SINCE 0 ? 4, LET THE 0 ALONE AND DROP THE REST
  ?12.90

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SIG FIGS

• IE
• ROUND 12.90909
• SINCE 9 ? 5, INCREASE THE 0
• TO 1 AND DROP THE REST ?12.91

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SCIENTIFIC NOTATION
47
SCI NOTATION

• SCIENCE DEALS WITH THE VERY SMALL AND
• THE VERY
• LARGE!!!

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SCI NOTATION

• SCIENCE
• INVOLVES
• MEASURE-
• MENT ?
• SIG FIGS

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SCI NOTATION

• SCI NOTN
• IN OUR CLASS
• THE EASY
• WAY

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SCI NOTATION

• GENERAL
• FORMAT
• 1gtgt10 X 10?

51
SCI NOTATION

• GENERAL
• FORMAT
• . X 10?

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SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• ONE DIGIT (1-9)

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SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• A DECIMAL

54
SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• TWO MORE DIGITS
• (CAN BE ZEROS)

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SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• TEN

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SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• TO
  SOME
• 
  EXPONENT

57
SCI NOTATION

• GENERAL
• FORMAT
• . X 10?
• 
  NOTE THE EXPONENT CAN BE POSITIVE OR IT CAN BE
  NEGATIVE

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SCI NOTATION

• . X 10?
• IF THE ORIGINAL NUMBER WAS
• ONE OR GREATER, THE EXPONENT IS POSITIVE
• IF THE ORIGINAL NUMBER WAS LESS THAN ONE, THE
  EXPONENT IS NEGATIVE

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SCI NOTATION

• . X 10? EXAMPLE
• 9,000,000,000 IS WRITTEN AS
• 9.00 X 109

60
SCI NOTATION

• . X 10? EXAMPLE
• .0000000009 IS WRITTEN AS
• 9.00 X 10-10

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SCI NOTATION

• MR. E.,
• HOW DID YOU DO THAT?

62
SCI NOTATION

• MOVE THE
• DECIMAL SO
• ONLY ONE
• DIGIT IS
• BEHIND IT

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SCI NOTATION

• 2. ROUND THE
• TWO DIGITS
• BEHIND THE
• DECIMAL TO
• THE NEAREST
• HUNDREDTH.

64
SCI NOTATION

• PLACE
• TIMES (X)
• AFTER THAT
• THREE DIGIT
• NUMBER.

65
SCI NOTATION

• RAISE THE
• EXPONENT TO
• THE NUMBER
• OF SPACES THE
• DECIMAL WAS
• MOVED IN STEP 1

66
SCI NOTATION

• 4. IF THE DECIMAL WAS MOVED LEFT, THE EXPONENT
  IS POSITIVE

67
SCI NOTATION

• 4. IF THE DECIMAL WAS MOVED RIGHT, THE EXPONENT
  IS NEGATIVE.

68
SCI NOTATION

• EXAMPLE
• 9,000,000,000.
• CURRENT DECIMAL

69
SCI NOTATION

• EXAMPLE
• 9,000,000,000.
• MOVES SO THAT ONLY ONE DIGIT IS IN FRONT OF THE
  DECIMAL

70
SCI NOTATION

• EXAMPLE
• 9.00
• ROUND THE TWO DIGITS BEHIND THE DECIMAL TO THE
  NEAREST HUNDREDTH

71
SCI NOTATION

• EXAMPLE
• 9.00 X 10
• ADD X 10 AS PART OF
• NEW NUMBER

72
SCI NOTATION

• EXAMPLE
• 9.00 X 109
• SINCE THE DECIMAL HAS BEEN MOVED 9 PLACES, RAISE
  TENS EXPONENT TO 9

73
SCI NOTATION

• EXAMPLE 9.00 X 109
• NOTE THE EXPONENT IS
• POSITIVE BECAUSE THE
• DECIMAL WAS MOVED
• LEFT ( BECAUSE THE
• ORIGINAL NUMBER WAS ?1.

74
SCI NOTATION

• EXAMPLE 2
• .0000000009.
• MOVE THE DECIMAL SO THAT ONLY ONE DIGIT IS IN
  FRONT OF IT

75
SCI NOTATION

• EXAMPLE
• 9.00
• ROUND THE TWO DIGITS BEHIND THE DECIMAL TO THE
  NEAREST HUNDREDTH

76
SCI NOTATION

• EXAMPLE
• 9.00 X 10
• ADD X 10 AS PART OF
• NEW NUMBER

77
SCI NOTATION

• EXAMPLE
• 9.00 X 10-10
• SINCE THE DECIMAL HAS BEEN MOVED 10 PLACES, RAISE
  TENS EXPONENT TO -10

78
SCI NOTATION

• EXAMPLE 9.00 X 10-10
• NOTE THE EXPONENT IS
• NEGATIVE BECAUSE THE
• DECIMAL WAS MOVED
• RIGHT ( BECAUSE THE
• ORIGINAL NUMBER WAS ?1.