ACCURACY AND PRECISION

ACCURACY: refers to how close a measured value is to an accepted value

PRECISION: refers to how close a series of measurements are to one another.

Three Three targets with targets with three arrows three 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?

In your own words define accuracy and precision?In your own words define accuracy and precision?

PERCENT ERROR

The ratio of an error to an accepted value

Percent error = error (accepted value – your value) accepted value X

100%

Significant FiguresSignificant Figures

The numbers reported in a The numbers reported in a measurement are limited by measurement are limited by the measuring toolthe measuring tool

Significant figures in a Significant figures in a measurement include the measurement include the known digits plus one known digits plus one estimated digitestimated digit

100 M Butterfly 2009 Olympics

Men's 100m Butterfly Final

Rank

1 United States Michael Phelps

OR 50.58

2 Serbia Milorad Cavic

50.59

3 Australia Andrew Lauterstein

51.12

4 United States Ian Crocker

51.13

HOW IMPORTA NT WERE SIGNIFICANT DIGITS (FIGURES) TO THESE PEOPLE??

One 1/100 th of a second meant Phelps becoming an American icon or just another Olympic swimmer

Counting Significant FiguresCounting Significant Figures

RULE 1. All non-zero digits in a measured number are RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding occurred.significant. Only a zero could indicate that rounding occurred.

Number of Significant Figures

38.15 cm38.15 cm 44

5.6 ft5.6 ft 22

65.6 lb65.6 lb ______

122.55 m122.55 m ___

Leading ZerosLeading Zeros

RULE 2. Leading zeros in decimal numbers RULE 2. Leading zeros in decimal numbers

are are NOTNOT significant. significant.Number of Significant Figures

0.008 mm0.008 mm 11

0.0156 oz0.0156 oz 33

0.0042 lb0.0042 lb ________

0.000262 mL 0.000262 mL ____

Sandwiched ZerosSandwiched Zeros

RULE 3. Zeros between nonzero numbers are RULE 3. Zeros between nonzero numbers are

significant. (They can not be rounded unless significant. (They can not be rounded unless

they are on an end of a number.)they are on an end of a number.)Number of Significant Figures

50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 lb0.702 lb ________

0.00405 m0.00405 m ____

Trailing ZerosTrailing ZerosRULE 4. Trailing zeros in numbers without RULE 4. Trailing zeros in numbers without

decimals are decimals are NOTNOT significant. They are significant. They are

only serving as place holders.only serving as place holders.

Number of Significant

Figures

25,000 in. 25,000 in. 22

200. yr200. yr 33

48,600 gal48,600 gal ________

25,005,000 g 25,005,000 g ________

Learning CheckLearning Check

A. Which answers contain 3 significant A. Which answers contain 3 significant figures?figures?1) 0.47601) 0.4760 2) 0.00476 2) 0.00476 3) 4760 3) 4760

B. All the zeros are significant inB. All the zeros are significant in

1) 0.00307 1) 0.00307 2) 25.300 2) 25.300 3) 2.050 x 3) 2.050 x 101033

C. 534,675 rounded to 3 significant figures isC. 534,675 rounded to 3 significant figures is1) 535 1) 535 2) 535,000 2) 535,000 3) 5.35 x 10 3) 5.35 x 1055

Learning CheckLearning Check

In which set(s) do both numbers contain In which set(s) do both numbers contain the the samesame number of significant figures?number of significant figures?

1) 22.0 and 22.00 1) 22.0 and 22.00

2) 400.0 and 40 2) 400.0 and 40

3) 0.000015 and 150,0003) 0.000015 and 150,000

Learning CheckLearning CheckState the number of significant figures in State the number of significant figures in each of the following:each of the following:

A. 0.030 mA. 0.030 m 1 1 2 2 3 3

B. 4.050 LB. 4.050 L 2 2 3 3 4 4

C. 0.0008 gC. 0.0008 g 1 1 2 2 4 4

D. 3.00 mD. 3.00 m 1 1 2 2 3 3

E. 2,080,000 beesE. 2,080,000 bees 3 3 5 5 7 7

Significant Numbers in Significant Numbers in CalculationsCalculations

A calculated answer cannot be more A calculated answer cannot be more precise than the measuring tool. precise than the measuring tool.

A calculated answer must match the A calculated answer must match the least precise measurement.least precise measurement.

Significant figures are needed for final Significant figures are needed for final answers fromanswers from

1) adding or subtracting1) adding or subtracting

2) multiplying or dividing2) multiplying or dividing

Adding and SubtractingAdding and Subtracting

The answer has the same number of The answer has the same number of decimal places as the measurement decimal places as the measurement with the fewest decimal places.with the fewest decimal places.

25.25.22 one decimal placeone decimal place

+ 1.+ 1.3434 two decimal placestwo decimal places

26.5426.54

answer 26.5answer 26.5 one decimal placeone decimal place

Learning CheckLearning Check

In each calculation, round the answer to In each calculation, round the answer to the correct number of significant figures.the correct number of significant figures.

A. 235.05 + 19.6 + 2.1 = A. 235.05 + 19.6 + 2.1 =

1) 256.751) 256.75 2) 256.8 2) 256.8 3) 3) 257257

B. 58.925 - 18.2B. 58.925 - 18.2 ==

1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 3) 40.740.7

Multiplying and Dividing

Your final Answer may have only the Your final Answer may have only the number of significant figures .. . . . . . number of significant figures .. . . . . . Matching least number of sig figs in Matching least number of sig figs in the numbers you are multiplying or the numbers you are multiplying or dividing dividing

Round (or add zeros) to the calculated Round (or add zeros) to the calculated answer until you have the same answer until you have the same number of significant figures as the number of significant figures as the measurement with the fewest measurement with the fewest significant figures.significant figures.

Learning CheckLearning Check

A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 3)

9.1989.198

B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 60 3) 60

C. C. 2.54 X 0.00282.54 X 0.0028 = =

0.0105 X 0.060 0.0105 X 0.060

1) 11.31) 11.3 2) 112) 11 3) 0.041 3) 0.041