17 Accuracy Precision Sig Figs

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Accuracy, Precision

and

Significant Figures

Our Objectives:

Be able to…

 Distinguish between

PRECISION and ACCURACY. Determine the number of sig figs in a

measurement.

 Round any measurement to a set number of sig figs.

 Use scientific notation when necessary.

Accuracy:



 This is the concept which deals with This is the concept which deals with whether a whether a

measurement is

measurement is correctcorrectwhen compared to the when compared to the

known value or standard for that particular

measurement.

measurement. 

 When a statement about accuracy is made, it When a statement about accuracy is made, it

often involves a statement about

often involves a statement about percent errorpercent error.. 

 Percent errorPercent erroris often expressed by the following is often expressed by the following

equation: equation: 100 %    al Experiment tal Experiemen Actual error

Precision:



 This is the concept which addresses This is the concept which addresses the degree of the degree of

exactness

exactnesswhen expressing a particular measurement.when expressing a particular measurement.



 The precision of any single measurement that is made The precision of any single measurement that is made

by an observer is limited by how precise the tool

(measuring instrument) is in terms of its smallest unit.

1 METER BAR

Summary: Accuracy & Precision

Accuracyrefers to how “correct” a measurement is; how close it is to the accepted value.

Precisionrefers to how exactly a measurement is reported; or how closely repeated measurements will agree.

A measurement can be precise, but inaccurate.

A measurement can be imprecise, but accurate.

Examples:

Balances

Kilogram bathroom scale. Decigram balance.

Significant Figures

Significant Figuresare ones that have been accurately measured.

Sample Problems:

How many significant digits are in each of the following?

a. 903.2 b. 0.0090 c. 0.007 d. 0.02 e. 90.3 f. 0.090 0

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Which Digits are

Significant Figures?

 Rule 1: All non-zero numbers are significant.

 Rule 2: All imbedded (flanked) zeroes are significant.

 Rule 3: Leading zeroes are never significant.

 Rule 4: Trailing zeroes are ONLY significant if there is a decimal point present in the number.

Yep…More Practice Problems

1. 3.0800

2. 0.00418

3. 7.09 x 10-5

4. 91,600

5. 0.003005

6. 3.200 x10 9

7. 250

8. 780,000

9. 0.0101

10. 0.00800

5 3 3 3 4 4 2 2 3 3

Significant Figures:



 When someone else has made a measurement, When someone else has made a measurement,

you have no control over the choice of the

measuring tool or the degree of precision

associated with the device used.

associated with the device used. 

 You must rely on a set of rules to tell you the You must rely on a set of rules to tell you the

degree of precision.

degree of precision. 

 Refer to the Refer to the ““Tutorial: Significant Figures, Tutorial: Significant Figures,

Precision, and Accuracy

Precision, and Accuracy””Handout (later)Handout (later)

What if I measured it?

You will be expected to use the rules for

significant figures

…

in all your calculations

…

.and in all of your measurements

Measurements



No measurement is exact; there is always

some uncertainty.



There are always two parts to a

measurement:

Numerical part

Unit/label

Measuring with a Meter Stick



We know the object is greater than 2 and

less than 3.



We know the object is greater than 0.8

and less than 0.9



We can also guess at one more place. So,

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Meter Stick Example 1



What length is indicated by the arrow?

• More than 4, less than 5.

• More than 0.5 but less than 0.6

• Guess at 0.00

• So, 4.50 cm.

Meter Stick Example 2



What length is indicated by the arrow?

9.40 cm

Meter Stick Example 3



What length is indicated by the arrow?

12.34 cm

Measuring with a

Thermometer



What is the

temperature?



Greater than 15, but

less than 16.



Guess one place. So,

0.0



Final answer = 15.0

°

C

Thermometer Example 1



What is the

temperature?

28.5 °C

Thermometer Example 2



What is the

temperature?

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Thermometer Example 3



What is the

temperature?

36.0 °C

Measuring with a

Graduated Cylinder



What is the volume?



Read to the bottom of

the meniscus.



Greater than 30, less

than 31.



Guess at one. So, 0.0



Answer 30.0 mL

Graduated Cylinder Example 1



What is the volume?

4.28 mL

Graduated Cylinder Example 2



What is the volume?

27.5 mL

Graduated Cylinder Example 3



What is the volume?

5.00 mL

Multiplication and Division with

Significant Figures



Rule: Your final answer cannot contain

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Significant Figures:

Multiplication and Division



Round to least amount of significant

figures

3.22 cm

X 2.1 cm

6.762 cm

The answer would then be 6.8cm

Practice

1.

2.5 x 3.42 =

2.

3.10 x 4.520 =

3.

2.33 x 6.085 x 2.1 =

4.

(4.52 x 10

-4

) / (3.980 x 10

-6

) =

5.

(3.4617 x 10

7

) / (5.61 x 10

-4

) =

6.

(2.34 x 10

2

)(0.012)(5.2345 x 10

5

) =

8.6 14.0

3.0 x 10 1

114

6.17 x 10 10

1500000

Adding and Subtracting with

Significant Figures



As always, the answer is never more

precise than the numbers used in the

math: you can never be more precise than

the least precise measurement.



In addition and subtraction,

only look at

the decimal portion of the number

.

Adding and Subtracting with

Significant Figures

Rules:

1. Count the number of significant digits in the decimal portion of each measured number. 2. Round the answer to the LEAST number of

places in the decimal portion.



Ex. 24.686 mEx. 24.686 m

2.343 m

+

+ 3.21_m_3.21_m_

30.239 m

The correct answer is 30.24 m

Practice

1. 3.461728 + 14.91 + 0.980001 + 5.2631 =

2. 23.1 + 4.77 + 125.39 + 3.581=

3. 22.101 – 0.9307=

4. 0.04216 – 0.0004134 =

5. 564321 – 264321=

24.61

156.8

21.170

0.04175

300000

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Our Goals: Be able to…

 Determine the number of sig figs in a measurement.

 Round any measurement to a set number of sig figs.