ch3-ppt-notes

3.1 Measurements and Their > Using and Expressing 

Uncertainty 

Measurements 

A measurement is a quantity that has 

both a number and a unit. 

Measurements are fundamental to the 

experimental sciences. For that reason, 

it is important to be able to make 

measurements and to decide whether a 

measurement is correct. 

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3.1 Measurements and Their > Using and Expressing 

Uncertainty 

Measurements 

In scientific notation, a 

given number is 

written as the product 

of two numbers: a 

coefficient and 10 

raised to a power. 

The number of stars in a 

galaxy is an example 

of an estimate that 

should be expressed 

in scientific notation. 

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© Copyright Pearson Prentice Hall 


3.1 

Measurements and Their 

Uncertainty 

> Accuracy, Precision, and Error 

3.1 Measurements and Their > Accuracy, Precision, and Error 

Uncertainty 

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. 

How do you evaluate accuracy and 

precision? 

• Precision is a measure of how close a 

series of measurements are to one another. 

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Uncertainty 


Uncertainty 

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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1


Uncertainty 

Determining Error 

• The accepted value is the correct value 

based on reliable references. 


Uncertainty 

The percent error is the absolute value of 

the error divided by the accepted value, 

multiplied by 100%. 

• 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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3.1 


Uncertainty 

> Accuracy, Precision, and Error 


Uncertainty 

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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3.1 


Uncertainty 

> Significant Figures in Measurements 

3.1 


Uncertainty 


Significant Figures in Measurements 

Why must measurements be reported to 

the correct number of significant 

figures? 

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Suppose you estimate a weight that is 

between 2.4 lb and 2.5 lb to be 2.46 lb. 

The first two digits (2 and 4) are known. 

The last digit (6) is an estimate and 

involves some uncertainty. All three 

digits convey useful information, 

however, and are called significant 

figures. 

The significant figures in a measurement 

include all of the digits that are known, 

plus a last digit that is estimated. 

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2

3.1 


Uncertainty 


3.1 


Uncertainty 


Measurements must always be 

reported to the correct number of 

significant figures because 

calculated answers often depend on 

the number of significant figures in 

the values used in the calculation. 

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Uncertainty 

> 

3.1 


Uncertainty 


• Cont... 

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3

Practice Problems 

for Conceptual Problem 3.1 

3.1 


Uncertainty 

> Significant Figures in Calculations 

Significant Figures in Calculations 

Problem Solving 3.2 Solve Problem 2 

with the help of an interactive guided 

tutorial. 

How does the precision of a 

calculated answer compare to 

the precision of the 

measurements used to obtain it? 

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3.1 


Uncertainty 

> Significant Figures in Calculations 

In general, a calculated answer 

cannot be more precise than the 

least precise measurement from 

which it was calculated. 

The calculated value must be 

rounded to make it consistent 

with the measurements from 

which it was calculated. 

3.1 Measurements and Their > Significant Figures in Calculations 

Uncertainty 

Rounding 

To round a number, you must first decide 

how many significant figures your 

answer should have. The answer 

depends on the given measurements 

and on the mathematical process used 

to arrive at the answer. 

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SAMPLE PROBLEM 

3.1 


3.1 

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for Sample Problem 3.1 


Uncertainty 

Addition and Subtraction 

The answer to an addition or subtraction 

calculation should be rounded to the 

same number of decimal places (not 

digits) as the measurement with the 

least number of decimal places. 



tutorial. 

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3.2 


3.2 

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Practice Problems for Sample Problem 3.2 


Uncertainty 

Multiplication and Division 

• In calculations involving multiplication and 

division, you need to round the answer to the 

same number of significant figures as the 

measurement with the least number of 

significant figures. 



tutorial. 

• The position of the decimal point has nothing 

to do with the rounding process when 

multiplying and dividing measurements. 

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5


3.3 


3.3 

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3.3 


Problem Solving 3.8 Solve 

Problem 8 with the help of an 

interactive guided tutorial. 

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Section Assessment 

Assess students’ understanding 

of the concepts in Section 3.1. 

3.1 Section Quiz 

1. In which of the following expressions is the 

number on the left NOT equal to the number 

on the right? 

Continue to: 

Section Quiz 

-or- 

Launch: 

a. 0.00456 × 10 –8 = 4.56 × 10 –11 

b. 454 × 10 –8 = 4.54 × 10 –6 

c. 842.6 × 10 4 = 8.426 × 10 6 

d. 0.00452 × 10 6 = 4.52 × 10 9 

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6


2. Which set of measurements of a 2.00-g 

standard is the most precise? 

a. 2.00 g, 2.01 g, 1.98 g 

b. 2.10 g, 2.00 g, 2.20 g 

c. 2.02 g, 2.03 g, 2.04 g 

d. 1.50 g, 2.00 g, 2.50 g 


3. A student reports the volume of a liquid as 

0.0130 L. How many significant figures are in 

this measurement? 

a. 2 

b. 3 

c. 4 

d. 5 

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END OF SHOW 

7

3.2 The International System > Measuring with SI Units 

of Units 

All measurements depend on units that serve as 

reference standards. The standards of 

measurement used in science are those of the 

metric system. 

3.2 The International System > Measuring with SI Units 

of Units 

The five SI base units commonly used 

by chemists are the meter, the kilogram, 

the kelvin, the second, and the mole. 

The International System of Units (abbreviated 

SI, after the French name, Le Système 

International d’Unités) is a revised version of the 

metric system. 

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3.2 The International System > Units and Quantities 

of Units 

Units and Quantities 

What metric units are commonly used to 

measure length, volume, mass, 

temperature and energy? 


of Units 

Units of Length 

In SI, the basic unit of length, or linear measure, 

is the meter (m). For very large or and very small 

lengths, it may be more convenient to use a unit 

of length that has a prefix. 

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of Units 

Common metric units of length include 

the centimeter, meter, and kilometer. 


of Units 

Units of Volume 

The SI unit of volume is the amount of space occupied by 

a cube that is 1 m along each edge. This volume is the 

cubic meter (m) 3 . A more convenient unit of volume for 

everyday use is the liter, a non-SI unit. 

KNOW THIS: 

A liter (L) is the volume of a cube that is 10 centimeters 

(10 cm) along each edge (10 cm × 10 cm × 10 cm = 1000 

cm 3 = 1 L). 

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of Units 

Common metric units of volume include 

the liter, milliliter, cubic centimeter, and 

microliter. 


of Units 

The volume of 20 drops of liquid from a 

medicine dropper is approximately 1 mL. 

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of Units 

A sugar cube has a volume of 1 cm 3 . 1 mL is 

the same as 1 cm 3 . 


of Units 

A gallon of milk has about twice the volume of a 

2-L bottle of soda. 

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of Units 

Units of Mass 

The mass of an object is measured in 

comparison to a standard mass of 1 kilogram 

(kg), which is the basic SI unit of mass. 


of Units 

Common metric units of mass include 

kilogram, gram, milligram, and 

microgram. 

A gram (g) is 1/1000 of a kilogram; the mass of 1 

cm 3 of water at 4°C is 1 g. 

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2


of Units 

Weight is a force that measures the pull on a 

given mass by gravity. 

The astronaut shown on the surface of the 

moon weighs one sixth of what he weighs on 

Earth. 


of Units 

Units of Temperature 

Temperature is a measure of 

how hot or cold an object is. 

Thermometers are used to 

measure temperature. 

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of Units 

Scientists commonly use two equivalent 

units of temperature, the degree Celsius 

and the kelvin. 


of Units 

On the Celsius scale, the freezing point of 

water is 0°C and the boiling point is 100°C. 

On the Kelvin scale, the freezing point of water 

is 273.15 kelvins (K), and the boiling point is 

373.15 K. 

The zero point on the Kelvin scale, 0 K, or 

absolute zero, is equal to −273.15 °C. 

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of Units 

Because one degree on the Celsius scale is 

equivalent to one kelvin on the Kelvin scale, 

converting from one temperature to another is 

easy. You simply add or subtract 273, as shown 

in the following equations. 


of Units 

Conversions Between the Celsius and Kelvin 

Scales 

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3


3.4 


3.4 

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3.4 


3.4 

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of Units 

Units of Energy 

Energy is the capacity to do work or to produce 

heat. 

The joule and the calorie are common 

units of energy. 




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of Units 

The joule (J) is the SI unit of energy. 

One calorie (cal) is the quantity of heat that 

raises the temperature of 1 g of pure water by 

1°C. 


of Units 

This house is equipped with solar panels. The 

solar panels convert the radiant energy from the 

sun into electrical energy that can be used to 

heat water and power appliances. 

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3.2 Section Quiz. 


of the concepts in Section 3.2. 

Continue to: 

Launch: 

-or- 

Section Quiz 


1. Which of the following is not a base SI unit? 

a. meter 

b. gram 

c. second 

d. mole 

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2. If you measured both the mass and weight of 

an object on Earth and on the moon, you 

would find that 

a. both the mass and the weight do not 

change. 

b. both the mass and the weight change. 

c. the mass remains the same, but the weight 

changes. 

d. the mass changes, but the weight remains 

the same. 


3. A temperature of 30 degrees Celsius is 

equivalent to 

a. 303 K. 

b. 300 K. 

c. 243 K. 

d. 247 K. 

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END OF SHOW 

6

3.3 Conversion Problems > Conversion Factors 

A conversion factor is a ratio of equivalent 

measurements. 

The ratios 100 cm/1 m and 1 m/100 cm are 

examples of conversion factors. 

Animation 3 

Conversion Problems > Conversion Factors 

Learn how to select the proper conversion 

factor and how to use it. 

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When a measurement is multiplied by 

a conversion factor, the numerical 

value is generally changed, but the 

actual size of the quantity measured 

remains the same. 


The scale of the micrograph is in nanometers. 

Using the relationship 10 9 nm = 1 m, you can write 

the following conversion factors. 

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3.3 Conversion Problems > Dimensional Analysis 

SAMPLE PROBLEM 3.5 

Dimensional analysis is a way to analyze and 

solve problems using the units, or dimensions, 

of the measurements. 

Dimensional analysis provides you 

with an alternative approach to 

problem solving. 

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1


3.5 


3.5 

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3.6 




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3.6 


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2


3.6 


For Sample Problem 3.6 




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3.3 

Conversion Problems > Converting Between Units 

3.3 


Converting Between Units 

What types of problems are easily 

solved by using dimensional 

analysis? 

Problems in which a measurement 

with one unit is converted to an 

equivalent measurement with another 

unit are easily solved using 

dimensional analysis. 

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3.7 


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3


3.7 


3.7 

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3.3 


Multistep Problems 

When converting between units, it is often 

necessary to use more than one conversion 

factor. Sample problem 3.8 illustrates the use of 

multiple conversion factors. 




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3.8 


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3.8 


3.8 

I don’t usually leave the “Evaluate” items in the 

PowerPoint BUT in this case, it is useful: 

Please think a moment about your answers in 

this (class or anywhere) to problems to make 

sure your conclusion seems at least logical. 

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3.3 Conversion Problems > Converting Between Units 

Converting Complex Units 

Many common measurements are expressed 

as a ratio of two units. If you use dimensional 

analysis, converting these complex units is just 

as easy as converting single units. It will just 

take multiple steps to arrive at an answer. 




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3.9 


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3.9 


3.9 

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of the concepts in Section 3.3 

Continue to: 

Section Quiz 

-or- 

Launch: 

Problem-Solving 3.37 Solve 



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1. 1 Mg = 1000 kg. Which of the following would 

be a correct conversion factor for this 

relationship? 

a. × 1000. 

b. × 1/1000. 

c. ÷ 1000. 

d. 1000 kg/1Mg. 

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2. The conversion factor used to convert joules to 

calories changes 

a. the quantity of energy measured but not the 

numerical value of the measurement. 

b. neither the numerical value of the measurement 

nor the quantity of energy measured. 

c. the numerical value of the measurement but not 

the quantity of energy measured. 

d. both the numerical value of the measurement and 

the quantity of energy measured. 

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6


3. How many µ g are in 0.0134 g? 

a. 1.34 × 10 –4 

b. 1.34 × 10 –6 

c. 1.34 × 10 6 


4. Express the density 5.6 g/cm 3 in kg/m 3 . 

a. 5.6 × 10 6 kg/m 3 

b. 5.6 × 10 3 kg/m 3 

c. 0.56 kg/m 3 

d. 0.0056 kg/m 3 

d. 1.34 × 10 4 © Copyright Pearson Prentice Hall 

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END OF SHOW 

7

3.4 

Density > Determining Density 

3.4 


Determining Density 

Density is the ratio of the mass of an object to 

its volume. 

What determines the density of a 

substance? 

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3.4 


3.4 


Each of these 10-g samples has a different 

volume because the densities vary. 

Density is an intensive property that 

depends only on the composition of a 

substance, not on the size of the 

sample. 

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3.4 



The density of corn oil is 

less than the density of 

corn syrup. For that 

reason, the oil floats on 

top of the syrup. 

Simulation 1 

Rank materials according to their densities. 

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1

3.4 

Density > Density and Temperature 


Experiments show that the volume of most 

substances increases as the temperature 

increases. Meanwhile, the mass remains 

the same. Thus, the density must change. 

The density of a substance generally 

decreases as its temperature 

increases. 

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2



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of the concepts in Section 3.4 

Continue to: 

Section Quiz 

-or- 

Launch: 




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3


1. If 50.0 mL of corn syrup have a mass of 68.7 

g, the density of the corn syrup is 

a. 0.737 g/mL. 

b. 0.727 g/mL. 

c. 1.36 g/mL. 

d. 1.37 g/mL. 


2. What is the volume of a pure gold coin that 

has a mass of 38.6 g? The density of gold is 

19.3 g/cm 3 . 

a. 0.500 cm 3 

b. 2.00 cm 3 

c. 38.6 cm 3 

d. 745 cm 3 

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3. As the temperature increases, the density of 

most substances 

a. increases. 

Concept Map 3 

Density > Concept map 

Solve the Concept Map with the help of an 


b. decreases. 

c. remains the same. 

d. increases at first and then decreases. 

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END OF SHOW 

4

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