DIFFERENTIATE: ACCURACY AND PRECISION

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DIFFERENTIATEACCURACY AND PRECISION
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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?
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Significant Figures
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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.

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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

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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

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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
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When to use Significant figures

• When a measurement is recorded only those digits
  that are dependable are written down.

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Always estimate ONE place past the smallest mark!
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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

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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

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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

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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 ___

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How many sig figs in 65.8 kg

1. 1
2. 2
3. 3
4. 4
5. 5

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How many sig figs in 122.55 m

1. 1
2. 2
3. 3
4. 4
5. 5

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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 ____

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How many sig figs in 0.0042 kg

1. 1
2. 2
3. 3
4. 4
5. 5

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How many sig figs in 0.000262 mL

1. 1
2. 2
3. 3
4. 4
5. 5

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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 ____

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How many sig figs in 0.702 kg

1. 1
2. 2
3. 3
4. 4
5. 5

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How many sig figs in 0.00405 m

1. 1
2. 2
3. 3
4. 4
5. 5

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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 ____

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How many sig figs in 48,600 L

1. 1
2. 2
3. 3
4. 4
5. 5

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How many sig figs in 48,600. L

1. 1
2. 2
3. 3
4. 4
5. 5

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How many sig figs in 25,005,000 g

1. 1
2. 2
3. 3
4. 4
5. 5

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Which answers contain 3 significant figures?

1. ) 0.4760
2. ) 0.004706
3. ) 4760

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All the zeros are significant in

1. .00370
2. 25,300
3. 2.050 x 103

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534,675 rounded to 3 significant figures is

1. 535
2. 535,000
3. 5.35 x 105

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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

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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

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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

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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

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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.

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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

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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

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How many sig figs?

• 7
• 40
• 0.5
• 0.00003
• 7 x 105
• 7,000,000

• 1
• 1
• 1
• 1
• 1
• 1

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How many sig figs here?

• 1.2
• 2100
• 56.76
• 4.00
• 0.0792
• 7,083,000,000

• 2
• 2
• 4
• 3
• 3
• 4

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How many sig figs here?

• 3401
• 2100
• 2100.0
• 5.00
• 0.00412
• 8,000,050,000

• 4
• 2
• 5
• 3
• 3
• 6

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Sig Figs?? 640

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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Sig Figs?? 200.0

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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Sig Figs?? 0.5200

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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Sig Figs?? 1.005

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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Sig Figs?? 10,000

1. 1
2. 2
3. 3
4. 4
5. 5
6. 6

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How many sig figs?

• 700
• 700.
• 700.00
• .007
• .00700

• 1
• 3
• 5
• 1
• 3

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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

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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

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Metric Prefixes