DIFFERENTIATE: ACCURACY AND PRECISION precis and sig figs3.pdf · How many sig figs in 0.00405 m 1...
Transcript of DIFFERENTIATE: ACCURACY AND PRECISION precis and sig figs3.pdf · How many sig figs in 0.00405 m 1...
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DIFFERENTIATE:
ACCURACY AND
PRECISION
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Three targets with three arrows each to shoot.
Can you hit the bull's-eye?
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:
APPROXIMATE (OR MEASURED): weight, height, mass, distance—anything MEASURED needs significance attached.
No measurement is perfect.
EXACT (counted items and conversion factors have unlimited significant digits): the amount of money in your account, jelly beans in a jar, etc. And #m in a km or in in a ft
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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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1 2 3
0% 0%0%
. 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 neighbor’s
answer? Why or why not?
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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 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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How many sig figs in 122.55 m
1 2 3 4 5
0% 0% 0%0%0%
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 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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How many sig figs in 0.000262 mL
1 2 3 4 5
0% 0% 0%0%0%
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 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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How many sig figs in 0.00405 m
1 2 3 4 5
0% 0% 0%0%0%
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 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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How many sig figs in 48,600. L
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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How many sig figs in 25,005,000 g
1 2 3 4 5
0% 0% 0%0%0%
1. 1
2. 2
3. 3
4. 4
5. 5
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Which answers contain 3
significant figures?
) 0
.4760
) 0
.004706
) 4
760
0% 0%0%
1. ) 0.4760
2. ) 0.004706
3. ) 4760
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All the zeros are significant in
.0037
25300
2.0
50 x 10...
0% 0%0%
1. .00370
2. 25,300
3. 2.050 x 103
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534,675 rounded to 3 significant figures is
535
535000
5.3
5 x 105
0% 0%0%
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?
22.0
and 22.0
...
400.0
and 4
0
0.0
00015 and 1...
0% 0%0%
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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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
Learning Check
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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 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
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Sig Figs?? 200.0
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
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Sig Figs?? 0.5200
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
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Sig Figs?? 1.005
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 6
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Sig Figs?? 10,000
1 2 3 4 5 6
0% 0% 0%0%0%0%
a) 1
b) 2
c) 3
d) 4
e) 5
f) 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