accuracy & precision two important points in measurement
TRANSCRIPT
![Page 1: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/1.jpg)
Accuracy & Precision
Two important points in measurement
![Page 2: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/2.jpg)
Accuracy and PrecisionAt the conclusion of our time together, you should be able to:
1. Explain the difference between the accuracy and precision
2. Give examples of accuracy and precision
![Page 3: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/3.jpg)
Accuracy
Accuracy = the extent to which a measured value agrees with a standard valueAccuracy of a device must be checkedDoes it read a proper accepted value?
Beware of Parallax – the apparent shift in position when viewed at a different angle.
![Page 4: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/4.jpg)
Graduated Cylinder – Meniscus and Parallax
![Page 5: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/5.jpg)
![Page 6: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/6.jpg)
Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0 cm?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
![Page 7: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/7.jpg)
Murphy's Lawsof
Science and Technology
Technology is dominated by those who manage what they do not understand.
![Page 8: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/8.jpg)
Precision
Precision = the degree of exactness of a measurement that is repeatedly recorded.
Which set is more precise?18.2 , 18.4 , 18.3517.9 , 18.3 , 18.8516.8 , 17.2 , 19.44
![Page 9: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/9.jpg)
Example: Precision
Who is more precise when measuring the same 17.0 cm book?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm
![Page 10: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/10.jpg)
Accuracy vs. Precision
High Accuracy
High Precision
High Precision
Low Accuracy
![Page 11: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/11.jpg)
Three Three targets targets with three with three arrows arrows each to each to shoot.shoot.
Can you hit the bull's-eye?Can you hit the bull's-eye?
Both accurate and precise
Precise but not accurate
Neither accurate nor precise
How do How do they they compare?compare?
Can you define accuracy vs. precision?Can you define accuracy vs. precision?
![Page 12: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/12.jpg)
Why Is There Uncertainty?
• Measurements are performed with instruments, and no instrument can read to an infinite number of
decimal places
•Which of the instruments below has the greatest uncertainty in measurement?
![Page 13: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/13.jpg)
The Scientific Methodbegins with
Questions about the World Around You.
Ever Wonder Why?...
Braille dots are on the keypads of drive-up ATM's?
![Page 14: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/14.jpg)
Accuracy and PrecisionLet’s see if you can:
1. Explain the difference between the accuracy and precision
2. Give examples of accuracy and precision
![Page 15: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/15.jpg)
Exit Quiz: Evaluate whether the following are precise, accurate or both.
Low Accuracy
Low Precision
Low Accuracy
High Precision
High Accuracy
High Precision
![Page 16: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/16.jpg)
Significant Figures
In Measurements
![Page 17: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/17.jpg)
Significant FiguresAt the conclusion of our time together, you should be able to:
1. Explain what significant figures are in a measurement
2. Determine the number of significant figures in any measurement
![Page 18: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/18.jpg)
Significant Figures
The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.
The numbers reported in a measurement are limited by the measuring tool.
![Page 19: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/19.jpg)
How many sig figs are there in a given measurement?
![Page 20: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/20.jpg)
Measurement and Significant Figures
Every experimental measurement has a degree of uncertainty.
The volume, V, at right is certain in the 10’s place, 10mL<V<20mL
The 1’s digit is also certain, 17mL<V<18mL
A best guess is needed for the tenths place.
![Page 21: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/21.jpg)
To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually is considered uncertain by plus or minus 1.
No further insignificant digits should be recorded.
The total number of digits used to express such a measurement is called the number of significant figures.
All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.
![Page 22: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/22.jpg)
Below are two measurements of the mass of the same object. The same quantity is being described at two
different levels of precision or certainty.
![Page 23: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/23.jpg)
15 Helpful Hints On The Lab Report from
Mr. T’s Vast Lab Experience!!!
Hint #5. A record of data is essential. It fools the instructor into thinking that you
were working.
![Page 24: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/24.jpg)
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- 0.08 cm
Length reported = 2.77 cm
or 2.76 cm
or 2.78 cm
![Page 25: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/25.jpg)
Known + Estimated Digits
In 2.77 cm…
• Known digits Known digits 2 2 and and 77 are 100% certain are 100% certain
• The third digit The third digit 77 is estimated (uncertain) is estimated (uncertain)
• In the reported length, all In the reported length, all threethree digits digits (2.77 cm) are significant including the (2.77 cm) are significant including the
estimated oneestimated one
![Page 26: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/26.jpg)
Learning Check
. l8. . . . I . . . . I9. . . . I . . . . I10. . cm
What is the length of the line?
1) 9.31 cm
2) 9.32 cm
3) 9.33 cm
How does your answer compare with your
neighbor’s answer? Why or why not?
![Page 27: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/27.jpg)
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
![Page 28: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/28.jpg)
Always estimate ONE place past the Always estimate ONE place past the smallest mark!smallest mark!
11.5 mL
![Page 29: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/29.jpg)
So how many sig figs are there in a given measurement?
52.8 mL
![Page 30: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/30.jpg)
Be Wary of Wealth and Success!!
Charles Schwab, president of the largest steel company, died a pauper.
Edward Hopson, president of the largest gas company, became insane.
Richard Whitney, president of the New York Stock Exchange, was released from prison to die at home.
Cosabee Rivermore, the Great Bear of Wall Street, died of suicide.
![Page 31: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/31.jpg)
Be Wary of Wealth and Success!!
Gene Sarazan, the U.S. Open and the PGA Golf Tournaments Champion, went on to live a full and happy life playing golf
and remaining solvent.
Conclusion: Stop worrying about business and start playing more
golf!!
![Page 32: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/32.jpg)
How to Determine Significant Figures in a Problem
Use the following rules:
![Page 33: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/33.jpg)
Rule #1
Every nonzero digit is significant
Examples:
24 = 2
3.56 = 3
7 = 1
![Page 34: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/34.jpg)
Rule #2 – Sandwiched 0’s
Zeros between non-zeros are significant
Examples:
7003 = 4
40.9 = 3
![Page 35: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/35.jpg)
Rule #3 – Leading 0’s
Zeros appearing in front of non-zero digits are not significant
• Act as placeholders• Can’t be dropped, show magnitude
Examples:0.00024 = 20.453 = 3
![Page 36: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/36.jpg)
Rule #4 – Trailing 0’s with DP
Zeros at the end of a number and to the right of a decimal point are significant.
Examples:
43.00 = 4
1.010 = 4
1.50 =3
![Page 37: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/37.jpg)
Rule #5 – Trailing 0’s without DP
Zeros at the end of a number and to the left of a decimal point aren’t significant
Examples:
300 = 1
27,300 = 3
![Page 38: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/38.jpg)
Easier Way to do Sig Figs!!
• Pacific/Atlantic
P A
If a decimal point is present, start on the Pacific (P) side and draw an arrow through the number
until you hit a non-zero digit. Count all numbers without an arrow through them.
If a decimal is absent, start on the Atlantic (A) side and draw an arrow through the number until
you hit a non-zero digit.
![Page 39: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/39.jpg)
Examples:
123.003 grams
decimal present, start on “P” side, draw arrow, count digits without an arrow through it.
Answer = 6
10,100 centimeters
Decimal absent, start on “A” side, draw an arrow, count digits without an arrow through it.
Answer = 3
![Page 40: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/40.jpg)
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
![Page 41: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/41.jpg)
Learning Check
A. Which answer(s) contain 3 significant figures?
1) 0.4760 2) 0.00476 3) 4760
B. All the zeros are significant in
1) 0.00307 2) 25.300 3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535 2) 535,000 3) 5.35 x 105
![Page 42: Accuracy & Precision Two important points in measurement](https://reader030.vdocuments.net/reader030/viewer/2022032611/56649e885503460f94b8c088/html5/thumbnails/42.jpg)
Learning Check
In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 m and 22.00 m
2) 400.0 m and 40 m
3) 0.000015 m and 150,000 m