differentiate: accuracy and precision three targets with three arrows each to shoot. can you hit the...

DIFFERENTIATE:

ACCURACY AND

PRECISION

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?

Can you define accuracy and precision?Can you define accuracy and precision?What would a bullseye with accuracy and What would a bullseye with accuracy and no precision look like?no precision look like?

Significant Figures

What 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, height—anything MEASURED….USE SIG FIGS!

No measurement is perfect.

Reading a MeterstickReading a Meterstick

. l. l22. . . . I . . . . I. . . . I . . . . I33 . . . .I . . . . I . . . .I . . . . I44. . cm. . cm

First digit (known)First digit (known) = 2 = 2 2.?? cm2.?? cm

Second digit (known)Second digit (known) = 0.7 = 0.7 2.7? cm2.7? cm

Third digit (estimated) between 0.05- 0.07Third digit (estimated) between 0.05- 0.07

Length reportedLength reported == 2.75 cm 2.75 cm

oror 2.74 cm 2.74 cm

oror 2.76 cm2.76 cm

Known + Estimated DigitsKnown + Estimated Digits

In 2.76 cm…In 2.76 cm…

• Known digitsKnown digits 2 andand 7 are 100% certainare 100% certain

• The third digit 6 is estimated (uncertain)The third digit 6 is estimated (uncertain)

• In the reported length, all three digits In the reported length, all three digits (2.76 cm) are significant including the (2.76 cm) are significant including the estimated oneestimated one

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

When to use Significant figures

•When a measurement is recorded only those digits that are dependable are written down.

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

Zero as a Measured NumberZero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?What is the length of the line?

First digitFirst digit 5.?? cm5.?? cm

Second digitSecond digit 55..0? cm0? cm

Last (estimated) digit isLast (estimated) digit is 5.05.00 cm0 cm

Enter question text...

1 2 3

0% 0%0%

. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?What is the length of the line?

1) 9.6 cm 1) 9.6 cm

2) 9.62 cm 2) 9.62 cm

3) 9.63 cm3) 9.63 cm

How does your answer How does your answer

compare with your neighbor’s compare with your neighbor’s

answer? Why or why not?answer? Why or why not?

1. 1

2. 2

3. 3

Significant FiguresSignificant Figures

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

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

Counting Significant FiguresCounting Significant Figures

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

Number of Significant Figures

38.15 cm38.15 cm 44

5.6 m5.6 m 22

65.6 kg65.6 kg ______

122.55 m122.55 m ___

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

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

Leading ZerosLeading Zeros

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

NOTNOT significant. significant.


0.008 mm0.008 mm 11

0.0156 mg0.0156 mg 33

0.0042 kg0.0042 kg ________

0.000262 mL 0.000262 mL ____

How many sig figs in 0.0042 kg0.0042 kg

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

How many sig figs in 0.000262 mL0.000262 mL

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

Sandwiched ZerosSandwiched Zeros

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

(They can not be rounded unless they are on an end of a (They can not be rounded unless they are on an end of a

number.)number.)


50.8 mm50.8 mm 33

2001 min2001 min 44

0.702 kg0.702 kg ________

0.00405 m0.00405 m ____

How many sig figs in 0.702 kg0.702 kg

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

How many sig figs in 0.00405 m0.00405 m

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

Trailing ZerosTrailing Zeros

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

decimals are NOT significant. They are only decimals are NOT significant. They are only

serving as place holders.serving as place holders.


25,000 cm 25,000 cm 22

200. yr200. yr 33

48,600 L48,600 L ________

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

How many sig figs in 48,600 L48,600 L

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

How many sig figs in 48,600. L48,600. L

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

How many sig figs in 25,005,000 g25,005,000 g

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

Which answers contain 3 Which answers contain 3 significant figures?significant figures?

) 0.4760

) 0.004706

) 4760

0% 0%0%

1.1. ) 0.4760) 0.4760

2.2. ) 0.004706) 0.004706

3.3. ) 4760) 4760

All the zeros are significant inAll the zeros are significant in

.003725300

2.050 x

10...

0% 0%0%

1. .00370

2. 25,300

3. 2.050 x 103

534,675 rounded to 3 534,675 rounded to 3 significant figures issignificant figures is

535

535000

5.35 x 105

0% 0%0%

1. 535

2. 535,000

3. 5.35 x 105

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

significant figures?significant figures?

22.0 and 22.0...

400.0 and 40

0.000015 and 1...

0% 0%0%

1.1. 22.0 and 22.0022.0 and 22.00

2.2. 400.0 and 40400.0 and 40

3.3. 0.000015 and 150,0000.000015 and 150,000

Significant Numbers in CalculationsSignificant Numbers in Calculations

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

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

Significant figures are needed for final answers Significant figures are needed for final answers fromfrom

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 decimal The answer has the same number of decimal places as the measurement with the fewest places as the measurement with the fewest decimal places.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 the In each calculation, round the answer to the correct number of significant figures.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) 2573) 257

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

1) 40.7251) 40.725 2) 40.73 2) 40.73 3) 40.73) 40.7

Multiplying and Dividing

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


A. 2.19 X 4.2 =A. 2.19 X 4.2 = 1) 91) 9 2) 9.2 2) 9.2 3) 9.1983) 9.198

B. 4.311 ÷ 0.07 =B. 4.311 ÷ 0.07 = 1)1) 61.5861.58 2) 62 2) 62 3) 603) 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

State the number of significant figures in each of the State the number of significant figures in each of the following: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


How many sig figs?

•7

•40

•0.5

•0.00003

•7 x 105

•7,000,000

•1

•1

•1

•1

•1

•1

How many sig figs here?

• 1.2

• 2100

• 56.76

• 4.00

• 0.0792

• 7,083,000,000

• 2

• 2

• 4

• 3

• 3

• 4


• 3401

• 2100

• 2100.0

• 5.00

• 0.00412

• 8,000,050,000

• 4

• 2

• 5

• 3

• 3

• 6

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

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

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

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

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

How many sig figs?

700

700.

700.00

.007

.00700

•1

•3

•5

•1

•3


• 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


• 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

Metric PrefixesMetric Prefixes

differentiate: accuracy and precision three targets with three arrows each to shoot. can you hit the...

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