DIFFERENTIATE: ACCURACY AND PRECISION precis and sig figs5.pdf · DIFFERENTIATE: ACCURACY AND PRECISION. Three targets ... How many sig figs here? ... •.070 x .910 •0.0791 x 33.1

DIFFERENTIATE:

ACCURACY AND

PRECISION

Three targets with three arrows each to shoot.

Can you hit the bull's-eye?

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?

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 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

Known + Estimated Digits

In 2.76 cm…

• 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

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!

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

Enter question text...

1 2 3

0% 0%0%

. 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 neighbor’s

answer? Why or why not?

Significant 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

Counting 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 ___

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 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 ____

How many sig figs in 0.0042 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 mL

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

Sandwiched 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 ____

How many sig figs in 0.702 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 m

1 2 3 4 5

0% 0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

5. 5

Trailing 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 ____

How many sig figs in 48,600 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. 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 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

significant figures?

) 0

.4760

) 0

.004706

) 4

760

0% 0%0%

1. ) 0.4760

2. ) 0.004706

3. ) 4760

All the zeros are significant in

.0037

25300

2.0

50 x 10...

0% 0%0%

1. .00370

2. 25,300

3. 2.050 x 103

534,675 rounded to 3 significant figures is

535

535000

5.3

5 x 105

0% 0%0%

1. 535

2. 535,000

3. 5.35 x 105

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

significant figures?

22.0

and 22.0

...

400.0

and 4

0

0.0

00015 and 1...

0% 0%0%

1. 22.0 and 22.00

2. 400.0 and 40

3. 0.000015 and 150,000

Significant 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

Adding 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

Learning 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

Multiplying 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.

Learning 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

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

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

How many sig figs here?

• 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

How 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

• 2

• 1

• 2

• 2

• 3

• 1

How 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

• 1

• 2

• 1

• 3

• 2

Metric Prefixes