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DIFFERENTIATE: ACCURACY AND PRECISION

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Title: Introduction to Chemistry and Measurement Subject: High School Chemistry Author: Neil Rapp Keywords: measurement, density, introduction Last modified by – PowerPoint PPT presentation

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Title: DIFFERENTIATE: ACCURACY AND PRECISION


1
DIFFERENTIATEACCURACY AND PRECISION
2
Can you hit the bull's-eye?
Three targets with three arrows each to shoot.
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do they compare?
Can you define accuracy and precision? What would
a bullseye with accuracy and no precision look
like?
3
Significant Figures
4
What is a significant figure?
  • There are 2 kinds of numbers
  • EXACT the amount of money in your account,
    jelly beans in a jar, etc.. Known with certainty
  • APPROXIMATE (OR MEASURED) weight,
    heightanything MEASURED.USE SIG FIGS!
  • ? No measurement is perfect.

5
Reading a Meterstick
  • . l2. . . . I . . . . I3 . . . .I . . . . I4. .
    cm
  • First digit (known) 2 2.?? cm
  • Second digit (known) 0.7 2.7? cm
  • Third digit (estimated) between 0.05- 0.07
  • Length reported 2.75 cm
  • or 2.74 cm
  • or 2.76 cm

6
Known Estimated Digits
  • In 2.76 cm
  • Known digits 2 and 7 are 100 certain
  • The third digit 6 is estimated (uncertain)
  • In the reported length, all three digits (2.76
    cm) are significant including the estimated one

7
When to use Significant figures
  • To a mathematician 21.70, or 21.700 is the same.

But, to a scientist 21.7cm and 21.70cm is NOT
the same
8
When to use Significant figures
  • When a measurement is recorded only those digits
    that are dependable are written down.

9
Always estimate ONE place past the smallest mark!
10
Zero as a Measured Number
  • . l3. . . . I . . . . I4 . . . . I . . . . I5. .
    cm
  • What is the length of the line?
  • First digit 5.?? cm
  • Second digit 5.0? cm
  • Last (estimated) digit is 5.00 cm

11
Enter question text...
. l8. . . . I . . . . I9. . . .I . . . . I10. .
cm What is the length of the line? 1) 9.6
cm 2) 9.62 cm 3) 9.63 cm How
does your answer compare with your neighbors
answer? Why or why not?
  1. 1
  2. 2
  3. 3

12
Significant Figures
  • The numbers reported in a measurement are limited
    by the measuring tool
  • Significant figures in a measurement include the
    known digits plus one estimated digit

13
Counting Significant Figures
  • RULE 1. All non-zero digits in a measured number
    are significant. Only a zero could indicate that
    rounding occurred.
  • Number of Significant Figures
  • 38.15 cm 4
  • 5.6 m 2
  • 65.6 kg ___
  • 122.55 m ___

14
How many sig figs in 65.8 kg
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

15
How many sig figs in 122.55 m
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

16
Leading Zeros
  • RULE 2. Leading zeros in decimal numbers are NOT
    significant.
  • Number of Significant Figures
  • 0.008 mm 1
  • 0.0156 mg 3
  • 0.0042 kg ____
  • 0.000262 mL ____

17
How many sig figs in 0.0042 kg
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

18
How many sig figs in 0.000262 mL
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

19
Sandwiched Zeros
  • RULE 3. Zeros between nonzero numbers are
    significant. (They can not be rounded unless they
    are on an end of a number.)
  • Number of Significant Figures
  • 50.8 mm 3
  • 2001 min 4
  • 0.702 kg ____
  • 0.00405 m ____

20
How many sig figs in 0.702 kg
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

21
How many sig figs in 0.00405 m
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

22
Trailing Zeros
  • RULE 4. Trailing zeros in numbers without
    decimals are NOT significant. They are only
    serving as place holders.
  • Number of Significant Figures
  • 25,000 cm 2
  • 200. yr 3
  • 48,600 L ____
  • 25,005,000 g ____

23
How many sig figs in 48,600 L
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

24
How many sig figs in 48,600. L
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

25
How many sig figs in 25,005,000 g
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

26
Which answers contain 3 significant figures?
  1. ) 0.4760
  2. ) 0.004706
  3. ) 4760

27
All the zeros are significant in
  1. .00370
  2. 25,300
  3. 2.050 x 103

28
534,675 rounded to 3 significant figures is
  1. 535
  2. 535,000
  3. 5.35 x 105

29
In which set(s) do both numbers contain the same
number of significant figures?
  1. 22.0 and 22.00
  2. 400.0 and 40
  3. 0.000015 and 150,000

30
Significant Numbers in Calculations
  • A calculated answer cannot be more precise than
    the measuring tool.
  • A calculated answer must match the least precise
    measurement.
  • Significant figures are needed for final answers
    from
  • 1) adding or subtracting
  • 2) multiplying or dividing

31
Adding and Subtracting
  • The answer has the same number of decimal places
    as the measurement with the fewest decimal
    places.
  • 25.2 one decimal place
  • 1.34 two decimal places
  • 26.54
  • answer 26.5 one decimal place

32
Learning Check
  • In each calculation, round the answer to the
    correct number of significant figures.
  • A. 235.05 19.6 2.1
  • 1) 256.75 2) 256.8 3) 257
  • B. 58.925 - 18.2
  • 1) 40.725 2) 40.73 3) 40.7

33
Multiplying and Dividing
  • Round (or add zeros) to the calculated answer
    until you have the same number of significant
    figures as the measurement with the fewest
    significant figures.

34
Learning Check
  • A. 2.19 X 4.2
  • 1) 9 2) 9.2 3) 9.198
  • B. 4.311 0.07
  • 1) 61.58 2) 62 3) 60
  • C. 2.54 X 0.0028
  • 0.0105 X 0.060
  • 1) 11.3 2) 11 3) 0.041

35
Learning Check
  • State the number of significant figures in each
    of the following
  • A. 0.030 m 1 2 3
  • B. 4.050 L 2 3 4
  • C. 0.0008 g 1 2 4
  • D. 3.00 m 1 2 3
  • E. 2,080,000 bees 3 5 7

36
How many sig figs?
  • 7
  • 40
  • 0.5
  • 0.00003
  • 7 x 105
  • 7,000,000
  • 1
  • 1
  • 1
  • 1
  • 1
  • 1

37
How many sig figs here?
  • 1.2
  • 2100
  • 56.76
  • 4.00
  • 0.0792
  • 7,083,000,000
  • 2
  • 2
  • 4
  • 3
  • 3
  • 4

38
How many sig figs here?
  • 3401
  • 2100
  • 2100.0
  • 5.00
  • 0.00412
  • 8,000,050,000
  • 4
  • 2
  • 5
  • 3
  • 3
  • 6

39
Sig Figs?? 640
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6

40
Sig Figs?? 200.0
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6

41
Sig Figs?? 0.5200
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6

42
Sig Figs?? 1.005
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6

43
Sig Figs?? 10,000
  1. 1
  2. 2
  3. 3
  4. 4
  5. 5
  6. 6

44
How many sig figs?
  • 700
  • 700.
  • 700.00
  • .007
  • .00700
  • 1
  • 3
  • 5
  • 1
  • 3

45
How many sig figs here?
  • 1.02 x 2.3
  • 210 x 200
  • 210. x 210
  • .070 x .910
  • 0.0791 x 33.1
  • 2.3x105 x 200
  • 2
  • 1
  • 2
  • 2
  • 3
  • 1

46
How many sig figs here?
  • 23 x 2 x 231
  • 455 x 21 x 25.2
  • 2100.0 x .0005
  • 5.00 x 311.22
  • 0.00412 x 9.1
  • 1
  • 2
  • 1
  • 3
  • 2

47
Metric Prefixes
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