Title: DIFFERENTIATE: ACCURACY AND PRECISION
1DIFFERENTIATEACCURACY AND PRECISION
2Can 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?
3Significant Figures
4What 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.
5Reading 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
6Known Estimated Digits
- 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
7When 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
8When to use Significant figures
- When a measurement is recorded only those digits
that are dependable are written down.
9Always estimate ONE place past the smallest mark!
10Zero 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
-
11Enter 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
- 2
- 3
12Significant 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
13Counting 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 ___
-
14How many sig figs in 65.8 kg
- 1
- 2
- 3
- 4
- 5
15How many sig figs in 122.55 m
- 1
- 2
- 3
- 4
- 5
16Leading 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 ____
17How many sig figs in 0.0042 kg
- 1
- 2
- 3
- 4
- 5
18How many sig figs in 0.000262 mL
- 1
- 2
- 3
- 4
- 5
19Sandwiched 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 ____
20How many sig figs in 0.702 kg
- 1
- 2
- 3
- 4
- 5
21How many sig figs in 0.00405 m
- 1
- 2
- 3
- 4
- 5
22Trailing 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 ____
23How many sig figs in 48,600 L
- 1
- 2
- 3
- 4
- 5
24How many sig figs in 48,600. L
- 1
- 2
- 3
- 4
- 5
25How many sig figs in 25,005,000 g
- 1
- 2
- 3
- 4
- 5
26Which answers contain 3 significant figures?
- ) 0.4760
- ) 0.004706
- ) 4760
27All the zeros are significant in
- .00370
- 25,300
- 2.050 x 103
28 534,675 rounded to 3 significant figures is
- 535
- 535,000
- 5.35 x 105
29In which set(s) do both numbers contain the same
number of significant figures?
- 22.0 and 22.00
- 400.0 and 40
- 0.000015 and 150,000
30Significant 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
31Adding 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
32Learning 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
33Multiplying 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.
34Learning 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
35Learning 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
36How many sig figs?
- 7
- 40
- 0.5
- 0.00003
- 7 x 105
- 7,000,000
37How many sig figs here?
- 1.2
- 2100
- 56.76
- 4.00
- 0.0792
- 7,083,000,000
38How many sig figs here?
- 3401
- 2100
- 2100.0
- 5.00
- 0.00412
- 8,000,050,000
39Sig Figs?? 640
- 1
- 2
- 3
- 4
- 5
- 6
40Sig Figs?? 200.0
- 1
- 2
- 3
- 4
- 5
- 6
41Sig Figs?? 0.5200
- 1
- 2
- 3
- 4
- 5
- 6
42Sig Figs?? 1.005
- 1
- 2
- 3
- 4
- 5
- 6
43Sig Figs?? 10,000
- 1
- 2
- 3
- 4
- 5
- 6
44How many sig figs?
- 700
- 700.
- 700.00
- .007
- .00700
45How 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
46How 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
47Metric Prefixes