Cmc chapter 02

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Analyzing Data

Section 2.1 Units and Measurements

Section 2.2 Scientific Notation and Dimensional Analysis

Section 2.3 Uncertainty in Data

Section 2.4 Representing Data

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the corresponding slides.

Section 2-1


• Define SI base units for time, length, mass, and temperature.

mass: a measurement that reflects the amount of matter an object contains

• Explain how adding a prefix changes a unit.

• Compare the derived units for volume and density.

Section 2-1

Section 2.1 Units and Measurements (cont.)

base unit

second

meter

kilogram

Chemists use an internationally recognized system of units to communicate their findings.

kelvin

derived unit

liter

density

Section 2-1

Units

• Système Internationale d'Unités (SI) is an internationally agreed upon system of measurements.

• A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world, and is independent of other units.

Section 2-1

Units (cont.)

Section 2-1

Units (cont.)

Section 2-1

Units (cont.)

• The SI base unit of time is the second (s), based on the frequency of radiation given off by a cesium-133 atom.

• The SI base unit for length is the meter (m), the distance light travels in a vacuum in 1/299,792,458th of a second.

• The SI base unit of mass is the kilogram (kg), about 2.2 pounds

Section 2-1

Units (cont.)

• The SI base unit of temperature is the kelvin (K).

• Zero kelvin is the point where there is virtually no particle motion or kinetic energy, also known as absolute zero.

• Two other temperature scales are Celsius and Fahrenheit.

Section 2-1

Derived Units

• Not all quantities can be measured with SI base units.

• A unit that is defined by a combination of base units is called a derived unit.

Section 2-1

Derived Units (cont.)

• Volume is measured in cubic meters (m3), but this is very large. A more convenient measure is the liter, or one cubic decimeter (dm3).

Section 2-1

Derived Units (cont.)

• Density is a derived unit, g/cm3, the amount of mass per unit volume.

• The density equation is density = mass/volume.

A. A

B. B

C. C

D. D

Section 2-1

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Section 2.1 Assessment

Which of the following is a derived unit?

A. yard

B. second

C. liter

D. kilogram

A. A

B. B

C. C

D. D

Section 2-1

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What is the relationship between mass and volume called?

A. density

B. space

C. matter

D. weight

End of Section 2-1

Section 2-2


• Express numbers in scientific notation.

quantitative data: numerical information describing how much, how little, how big, how tall, how fast, and so on

• Convert between units using dimensional analysis.

Section 2-2

Section 2.2 Scientific Notation and Dimensional Analysis (cont.)

scientific notation

dimensional analysis

conversion factor

Scientists often express numbers in scientific notation and solve problems using dimensional analysis.

Section 2-2

Scientific Notation

• Scientific notation can be used to express any number as a number between 1 and 10 (the coefficient) multiplied by 10 raised to a power (the exponent).

• Count the number of places the decimal point must be moved to give a coefficient between 1 and 10.

Section 2-2

Scientific Notation (cont.)

800 = 8.0 102

0.0000343 = 3.43 10–5

• The number of places moved equals the value of the exponent.

• The exponent is positive when the decimal moves to the left and negative when the decimal moves to the right.

Section 2-2


• Addition and subtraction

– Exponents must be the same.

– Rewrite values with the same exponent.

– Add or subtract coefficients.

Section 2-2


• Multiplication and division

– To multiply, multiply the coefficients, then add the exponents.

– To divide, divide the coefficients, then subtract the exponent of the divisor from the exponent of the dividend.

Section 2-2

Dimensional Analysis

• Dimensional analysis is a systematic approach to problem solving that uses conversion factors to move, or convert, from one unit to another.

• A conversion factor is a ratio of equivalent values having different units.

Section 2-2

Dimensional Analysis (cont.)

• Writing conversion factors

– Conversion factors are derived from equality relationships, such as 1 dozen eggs = 12 eggs.

– Percentages can also be used as conversion factors. They relate the number of parts of one component to 100 total parts.

Section 2-2

Dimensional Analysis (cont.)

• Using conversion factors

– A conversion factor must cancel one unit and introduce a new one.

A. A

B. B

C. C

D. D

Section 2-2

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What is a systematic approach to problem solving that converts from one unit to another?

A. conversion ratio

B. conversion factor

C. scientific notation

D. dimensional analysis

A. A

B. B

C. C

D. D

Section 2-2


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Which of the following expresses 9,640,000 in the correct scientific notation?

A. 9.64 104

B. 9.64 105

C. 9.64 × 106

D. 9.64 610

End of Section 2-2

Section 2-3


• Define and compare accuracy and precision.

experiment: a set of controlled observations that test a hypothesis

• Describe the accuracy of experimental data using error and percent error.

• Apply rules for significant figures to express uncertainty in measured and calculated values.

Section 2-3

Section 2.3 Uncertainty in Data (cont.)

accuracy

precision

error

Measurements contain uncertainties that affect how a result is presented.

percent error

significant figures

Section 2-3

Accuracy and Precision

• Accuracy refers to how close a measured value is to an accepted value.

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

Section 2-3

Accuracy and Precision (cont.)

• Error is defined as the difference between and experimental value and an accepted value.

Section 2-3

Accuracy and Precision (cont.)

• The error equation is error = experimental value – accepted value.

• Percent error expresses error as a percentage of the accepted value.

Section 2-3

Significant Figures

• Often, precision is limited by the tools available.

• Significant figures include all known digits plus one estimated digit.

Section 2-3

Significant Figures (cont.)

• Rules for significant figures

– Rule 1: Nonzero numbers are always significant.

– Rule 2: Zeros between nonzero numbers are always significant.

– Rule 3: All final zeros to the right of the decimal are significant.

– Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.

– Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

Section 2-3

Rounding Numbers

• Calculators are not aware of significant figures.

• Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

Section 2-3

Rounding Numbers (cont.)

• Rules for rounding

– Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure.

– Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure.

– Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure.

Section 2-3


• Rules for rounding (cont.)

– Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up.

Section 2-3


• Addition and subtraction

– Round numbers so all numbers have the same number of digits to the right of the decimal.

• Multiplication and division

– Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

A. A

B. B

C. C

D. D

Section 2-3

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Determine the number of significant figures in the following: 8,200, 723.0, and 0.01.

A. 4, 4, and 3

B. 4, 3, and 3

C. 2, 3, and 1

D. 2, 4, and 1

A. A

B. B

C. C

D. D

Section 2-3


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A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error?

A. 20%

B. –20%

C. 10%

D. 90%

End of Section 2-3

Section 2-4


• Create graphics to reveal patterns in data.

independent variable: the variable that is changed during an experiment

graph

• Interpret graphs.

Graphs visually depict data, making it easier to see patterns and trends.

Section 2-4

Graphing

• A graph is a visual display of data that makes trends easier to see than in a table.

Section 2-4

Graphing (cont.)

• A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

Section 2-4

Graphing (cont.)

• Bar graphs are often used to show how a quantity varies across categories.

Section 2-4

Graphing (cont.)

• On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

Section 2-4

Graphing (cont.)

• If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.

Section 2-4

Interpreting Graphs

• Interpolation is reading and estimating values falling between points on the graph.

• Extrapolation is estimating values outside the points by extending the line.

Section 2-4

Interpreting Graphs (cont.)

• This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.

A. A

B. B

C. C

D. D

Section 2-4

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____ variables are plotted on the ____-axis in a line graph.

A. independent, x

B. independent, y

C. dependent, x

D. dependent, z

A. A

B. B

C. C

D. D

Section 2-4


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What kind of graph shows how quantities vary across categories?

A. pie charts

B. line graphs

C. Venn diagrams

D. bar graphs

End of Section 2-4

Resources Menu

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Study Guide

Chapter Assessment

Standardized Test Practice

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Concepts in Motion

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Study Guide 1


Key Concepts

• SI measurement units allow scientists to report data to other scientists.

• Adding prefixes to SI units extends the range of possible measurements.

• To convert to Kelvin temperature, add 273 to the Celsius temperature. K = °C + 273

• Volume and density have derived units. Density, which is a ratio of mass to volume, can be used to identify an unknown sample of matter.

Study Guide 2


Key Concepts

• A number expressed in scientific notation is written as a coefficient between 1 and 10 multiplied by 10 raised to a power.

• To add or subtract numbers in scientific notation, the numbers must have the same exponent.

• To multiply or divide numbers in scientific notation, multiply or divide the coefficients and then add or subtract the exponents, respectively.

• Dimensional analysis uses conversion factors to solve problems.

Study Guide 3


Key Concepts

• An accurate measurement is close to the accepted value. A set of precise measurements shows little variation.

• The measurement device determines the degree of precision possible.

• Error is the difference between the measured value and the accepted value. Percent error gives the percent deviation from the accepted value.

error = experimental value – accepted value

Study Guide 3

Section 2.3 Uncertainty in Data (cont.)

Key Concepts

• The number of significant figures reflects the precision of reported data.

• Calculations should be rounded to the correct number of significant figures.

Study Guide 4


Key Concepts

• Circle graphs show parts of a whole. Bar graphs show how a factor varies with time, location, or temperature.

• Independent (x-axis) variables and dependent (y-axis) variables can be related in a linear or a nonlinear manner. The slope of a straight line is defined as rise/run, or ∆y/∆x.

• Because line graph data are considered continuous, you can interpolate between data points or extrapolate beyond them.

A. A

B. B

C. C

D. D

Chapter Assessment 1

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Which of the following is the SI derived unit of volume?

A. gallon

B. quart

C. m3

D. kilogram

A. A

B. B

C. C

D. D


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Which prefix means 1/10th?

A. deci-

B. hemi-

C. kilo-

D. centi-

A. A

B. B

C. C

D. D


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Divide 6.0 109 by 1.5 103.

A. 4.0 106

B. 4.5 103

C. 4.0 103

D. 4.5 106

A. A

B. B

C. C

D. D


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Round the following to 3 significant figures 2.3450.

A. 2.35

B. 2.345

C. 2.34

D. 2.40

A. A

B. B

C. C

D. D


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The rise divided by the run on a line graph is the ____.

A. x-axis

B. slope

C. y-axis

D. y-intercept

A. A

B. B

C. C

D. D

STP 1

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Which is NOT an SI base unit?

A. meter

B. second

C. liter

D. kelvin

A. A

B. B

C. C

D. D

STP 2

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Which value is NOT equivalent to the others?

A. 800 m

B. 0.8 km

C. 80 dm

D. 8.0 x 105 cm

A. A

B. B

C. C

D. D

STP 3

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Find the solution with the correct number of significant figures:25 0.25

A. 6.25

B. 6.2

C. 6.3

D. 6.250

A. A

B. B

C. C

D. D

STP 4

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How many significant figures are there in 0.0000245010 meters?

A. 4

B. 5

C. 6

D. 11

A. A

B. B

C. C

D. D

STP 5

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Which is NOT a quantitative measurement of a liquid?

A. color

B. volume

C. mass

D. density

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Table 2.2 SI Prefixes

Figure 2.10 Accuracy and Precision

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Cmc chapter 02