Chapter 2 Measurements and Calculations. Section 2.1 Scientific Notation Return to TOC Copyright © Cengage Learning. All rights reserved Measurement Quantitative

Chapter 2

Measurements and Calculations

Section 2.1

Scientific Notation

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Copyright © Cengage Learning. All rights reserved

Measurement

• Quantitative observation.• Has 2 parts – number

and unit.

Section 2.1

Scientific Notation

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• Technique used to express very large or very small numbers.

• Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

Section 2.1

Scientific Notation

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Using Scientific Notation

• The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative.

Section 2.1

Scientific Notation

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Using Scientific Notation

• If the decimal point is moved to the left, the power of 10 is positive.

• If the decimal point is moved to the right, the power of 10 is negative.

Section 2.1

Scientific Notation

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1. The World’s population is estimated to be 7,187,000,000 people. Express this number in scientific notation.

2. Express the following numbers in scientific notation: 0.0000671; 72.

3. Express the following numbers in standard notation: 2.598 x 10-7; 9.5 x 104.

Section 2.2

Units

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Nature of Measurement

Section 2.2

Units

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The Fundamental SI Units

Physical Quantity Name of Unit Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature kelvin K

Electric current ampere A

Amount of substance mole mol

Section 2.2

Units

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Prefixes Used in the SI System

Section 2.3

Measurements of Length, Volume, and Mass

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Length

Section 2.3


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Volume

• Measure of the amount of 3-D space occupied by a substance.

Section 2.3


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Mass

• Measure of the amount of matter present in an object.

Weight

• Measure of the gravitational pull on

an object.

Section 2.3


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Concept Check

Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)?

A gallon of milk is equal to about 4 L of milk. A 200-lb man has a mass of about 90 kg. A basketball player has a height of 7 m tall. A nickel is 6.5 cm thick.

Section 2.4

Uncertainty in Measurement

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Measurement of Length Using a Ruler

Section 2.4

Uncertainty in Measurement

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• A digit that must be estimated is called uncertain.

• A measurement always has some degree of uncertainty.

• Record the certain digits and the first uncertain digit (the estimated number).

Section 2.5

Significant Figures

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Nonzero integers always count as significant figures.

Rules for Counting Significant Figures

Section 2.5

Significant Figures

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1. Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures.

2. Captive zeros are zeros between nonzero digits. These always count as significant figures.

3. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point.


Section 2.5

Significant Figures

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Exponential Notation

Section 2.5

Significant Figures

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Exact numbers have an infinite number of significant figures.


Section 2.5

Significant Figures

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1. If the digit to be removed is less than 5, the preceding digit stays the same. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1.

2. In a series of calculations, carry the extra digits through to the final result and then round off.

Rules for Rounding Off

Section 2.5

Significant Figures

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1. For multiplication or division, the number of significant figures in the result is the same as that in the measurement with the smallest number of significant figures.

Significant Figures in Mathematical Operations

Section 2.5

Significant Figures

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2. For addition or subtraction, the limiting term is the one with the smallest number of decimal places.

Significant Figures in Mathematical Operations

Section 2.5

Significant Figures

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Concept Check

You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred).

How would you write the number describing the total volume?

What limits the precision of the total volume?

Section 2.5

Significant Figures

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1. An impossibly regular, paved walkway mysteriously appears overnight; leading out of Seattle. Careful measurement shows this walkway to be 15,432 meters long and 0.42 meters wide. To the correct number of significant figures, what area is covered by walkway? How would this number change if the walkway were 0.41 meters wide? 0.43 meters wide?

2. By the next morning, this walkway has grown 0.42 meters. To the correct number of significant figures, how long is it now?

Section 2.6

Problem Solving and Dimensional Analysis

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• Use when converting a given result from one system of units to another.

Section 2.5

Significant Figures

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1. A golfer putted a golf ball 6.8 ft across a green. How many inches does this represent? How many centimeters?

2. What is the volume of a 1.25 gallon jug in cubic centimeters? Cubic inches? (1 L = 1.057 qts)

3. An iron sample has a mass of 4.50 lb. What is the mass of this sample in grams? (1 kg = 2.2046 lbs)

4. If an oxygen molecule is moving at 4.78 x 104 cm/s, what is its speed in mi/hr?

Section 2.7

Temperature Conversions: An Approach to Problem Solving

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• Fahrenheit• Celsius• Kelvin

Three Systems for Measuring Temperature

Section 2.7


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The Three Major Temperature Scales

Section 2.7


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• Converting between scales

1. The normal body temperature for a dog is approximately 102oF. What is this equivalent to on the Kelvin temperature scale?

2. At what temperature does C = F?

Converting Between Scales

K C C K

FC F C

+ 273 273

32 1.80 + 32

1.80

T T T T

TT T T

Section 2.8

Density

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• Mass of substance per unit volume of the substance.

massDensity =

volume

Section 2.8

Density

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Section 2.8

Density

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Measuring the Volume of a Solid Object by Water Displacement

Section 2.8

Density

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Example

1. A certain mineral has a mass of 17.8 g and a volume of 2.35 cm3. What is the density of

this mineral?

2. What is the mass of a 49.6 mL sample of a liquid, which has a density of 0.85 g/mL?

3. Copper has a density of 8.96 g/cm3. If 75.0 g of copper is added to 50.0 mL of water in a

graduated cylinder, to what volume reading will the water level in the cylinder rise?

Section 2.8

Density

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Section 2.8

Density

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Section 2.8

Density

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Summary of Topics: Chapter 2

• Significant figures• Scientific notation• Metric units• Measured numbers, exact numbers• Dimensional analysis (conversions)• Temperature• Density

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Chapter 2 Measurements and Calculations. Section 2.1 Scientific Notation Return to TOC Copyright © Cengage Learning. All rights reserved Measurement Quantitative