© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 1 of 48 Using and Expressing Measurements How do measurements relate to science?

© Copyright Pearson Prentice Hall

Measurements and Their Uncertainty

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Slide 1 of 48

Using and Expressing Measurements

Using and Expressing Measurements

How do measurements relate to science?

3.1



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Slide 2 of 48

3.1 Using and Expressing Measurements

A measurement is a quantity that has both a number and a unit.

it is important to be able to make measurements and to decide whether a measurement is correct.



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Slide 3 of 48

Scientific Notation

http://www.youtube.com/watch?v=H578qUeoBC0

Scientific Notation Pre-Test



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Slide 4 of 48

Scientific Notation

210, 000,000,000,000,000,000,000

This number is written in decimal notation. When numbers get this large,

it is easier to write it in scientific notation

Where is the decimal in this number?



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Slide 5 of 48

210, 000,000,000,000,000,000,000.

Decimal needs moved to the left between the 2 and the 1 ( numbers that are

between 1-10)

When the original number is more than 1 the exponent will be positive.

2.1 x 1023

Exponents show how many places decimal was moved



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Express 4.58 x 106 in decimal notation

Remember the exponent tells you how many places to move the decimal. The exponent is positive so the decimal is moved to the right

4,580, 000



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Slide 7 of 48

express the number 0.000000345 in scientific notation.

Decimal moved between first 2 non-zero digits and will be moved 7 times

3.45 x 10 -7

The exponent is negative because the original number is a very small number



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Slide 8 of 48

Express the Express the following in following in

scientific notation scientific notation or standard or standard

notationnotation

1. 74171.71. 74171.7 2. .078822. .07882

3. 5263. 526 4. .00005734. .0000573

5. 5.8 x 10 5. 5.8 x 10 -7-7 6. 5.256 x 106. 5.256 x 1066



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Slide 9 of 48

Accuracy, Precision, and Error

Accuracy, Precision, and Error

What is the difference between accuracy and precision?

3.1



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Slide 10 of 48

3.1 Accuracy, Precision, and Error

Accuracy and Precision

• Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.

• Precision is a measure of how close a series of measurements are to one another.



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To evaluate the accuracy of a measurement, the measured value must be compared to the correct value.

To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.



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Determining Error

• The accepted (Known) value is the correct value based on reliable references.

• The experimental value is the value measured in the lab.

• The difference between the experimental value and the accepted value is called the error.



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The percent error is the absolute value of the error divided by the accepted value, multiplied by 100%.

Experimental – known



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Accuracy, Precision, and Error3.1

Percent Error

(Error) 3.00-measurement X 100

3.00



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Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.



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REVIEW



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REVIEW



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% ERROR

The density of aluminum is known to be 2.7 g/ml. In the lab you calculated the density of aluminum to be 2.4 g/ml. What is your percent error?

• What is 5.256X10-6 in standard format

• What is 118000 in scientific notation



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Slide 20 of 48

Significant Figures in Measurements

All measurement contains some degree of uncertainty.

The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.

Measurements must always be reported to the correct number of significant figures

Using pages 66-72 – fill in your notes regarding the rules of significant figures

3.1



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Slide 21 of 48

Timberlake lecture plus 21

Number of Significant Figures

38.15 cm 4

5.6 ft 2

65.6 lb ___

122.55 m ___

Complete: All non-zero digits in a measured number are (significant or not significant).

Counting Significant Figures



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Slide 22 of 48



0.008 mm 1

0.0156 oz 3

0.0042 lb ____

0.000262 mL ____

Complete: Leading zeros in decimal numbers are

(significant or not significant).

Leading Zeros



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50.8 mm 3

2001 min 4

0.702 lb ____

0.00405 m ____

Complete: Zeros between nonzero numbers

are (significant or not significant).

Sandwiched Zeros



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25,000 in. 2

200 yr 1

48,600 gal 3

25,005,000 g ____

Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.

Trailing Zeros



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A. Which answers 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



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Significant Figures 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



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Adding & 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



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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



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Solution

A. 235.05 + 19.6 + 2.1 =

2) 256.8

B. 58.925 - 18.2 =

3) 40.7



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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.



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Multiplication + Division

Answer should have the same number of significant figures as the measurement with the least.

You may need to round your answer in order to achieve this



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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



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Solution A. 2.19 X 4.2 = 2) 9.2

B. 4.311 ÷ 0.07 = 3) 60

C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060

Continuous calculator operation =

2.54 x 0.0028 0.0105 0.060



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Slide 34 of 48

3.1 Significant Figures in Calculations

Rounding

To round a number, you must first decide how many significant figures your answer should have.

Your answer should be rounded to the number with the least amount of significant figures



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Slide 35 of 48

QUIZ

1. How many significant figures are in the number

a. 603.040 b. 0.0828 c. 690,000

2. Perform the following operations and report to the correct number of sig. figs

a. 4.15 cm X 1.8 cm

b. 36.47 + 2.721 + 15.1

c. 5.6 x 107 x 3.60 x 10-3


SAMPLE PROBLEM

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3.1


SAMPLE PROBLEM

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3.1


SAMPLE PROBLEM

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3.2


SAMPLE PROBLEM

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3.2


SAMPLE PROBLEM

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3.3


SAMPLE PROBLEM

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3.3

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© Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 1 of 48 Using and Expressing Measurements How do measurements relate to science?