Accuracy & Precision

Accuracy & Precision

Two important points in measurement

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

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.

Graduated Cylinder – Meniscus and Parallax

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

Murphy's Lawsof

Science and Technology

Technology is dominated by those who manage what they do not understand.

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

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

Accuracy vs. Precision

High Accuracy

High Precision

High Precision

Low Accuracy

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?

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?

The Scientific Methodbegins with

Questions about the World Around You.

Ever Wonder Why?...

Braille dots are on the keypads of drive-up ATM's?

Accuracy and PrecisionLet’s see if you can:

1. Explain the difference between the accuracy and precision

2. Give examples of accuracy and precision

Exit Quiz: Evaluate whether the following are precise, accurate or both.

Low Accuracy

Low Precision

Low Accuracy

High Precision

High Accuracy

High Precision

Significant Figures

In Measurements

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

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.

How many sig figs are there in a given measurement?

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.

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.

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.

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.

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

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

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?

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

Always estimate ONE place past the Always estimate ONE place past the smallest mark!smallest mark!

11.5 mL

So how many sig figs are there in a given measurement?

52.8 mL

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.

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!!

How to Determine Significant Figures in a Problem

Use the following rules:

Rule #1

Every nonzero digit is significant

Examples:

24 = 2

3.56 = 3

7 = 1

Rule #2 – Sandwiched 0’s

Zeros between non-zeros are significant

Examples:

7003 = 4

40.9 = 3

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

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

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

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.

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

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

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

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