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Section 2.1Units and Measurements

Section 2.2Scientific Notation and Dimensional Analysis

Section 2.3Uncertainty in Data

Section 2.4Representing Data

Click a hyperlink or folder tab to view the corresponding slides.

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Chapter MenuSection 2.1 Units and Measurements

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

- Explain how adding a prefix changes a unit.
- Compare the derived units for volume and density.

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

Section 2-1Section 2.1 Units and Measurements (cont.)

base unit

second

meter

kilogram

kelvin

derived unit

liter

density

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

Section 2-1- 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.

Units (cont.)

Section 2-1Units (cont.)

Section 2-1Units (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

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.

- 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.

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).

Derived Units (cont.)

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

- The density equation is density = mass/volume.

B

C

D

Section 2.1 Assessment

Which of the following is a derived unit?

A.yard

B.second

C.liter

D.kilogram

Section 2-1B

C

D

Section 2.1 Assessment

What is the relationship between mass and volume called?

A.density

B.space

C.matter

D.weight

Section 2-1Section 2.2 Scientific Notation and Dimensional Analysis

- Express numbers in scientific notation.

- Convert between units using dimensional analysis.

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

Section 2-2Section 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 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.

Scientific Notation (cont.)

- 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.

800 = 8.0 102

0.0000343 = 3.43 10–5

Section 2-2Scientific Notation (cont.)

- Addition and subtraction

- Exponents must be the same.
- Rewrite values with the same exponent.
- Add or subtract coefficients.

Scientific Notation (cont.)

- 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.

- 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.

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.

Dimensional Analysis (cont.)

- Using conversion factors

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

B

C

D

Section 2.2 Assessment

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

Section 2-2B

C

D

Section 2.2 Assessment

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

Section 2-2Section 2.3 Uncertainty in Data

- Define and compare accuracy and precision.

- Describe the accuracy of experimental data using error and percent error.
- Apply rules for significant figures to express uncertainty in measured and calculated values.

experiment: a set of controlled observations that test a hypothesis

Section 2-3Section 2.3 Uncertainty in Data (cont.)

accuracy

precision

error

percent error

significant figures

Measurements contain uncertainties that affect how a result is presented.

Section 2-3- 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.

Accuracy and Precision (cont.)

- Erroris defined as the difference between and experimental value and an accepted value.

Accuracy and Precision (cont.)

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

- Percent errorexpresses error as a percentage of the accepted value.

- Often, precision is limited by the tools available.

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

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.

- 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.

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.

Rounding Numbers (cont.)

- 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.

Rounding Numbers (cont.)

- 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.

B

C

D

Section 2.3 Assessment

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

Section 2-3B

C

D

Section 2.3 Assessment

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.0.20 g/L

B.–0.20 g/L

C.0.10 g/L

D.0.90 g/L

Section 2-3- Create graphics to reveal patterns in data.

independent variable: the variable that is changed during an experiment

- Interpret graphs.

graph

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

Section 2-4- A graphis a visual display of data that makes trends easier to see than in a table.

Graphing (cont.)

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

Graphing (cont.)

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

Graphing (cont.)

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

Graphing (cont.)

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

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

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

Interpreting Graphs (cont.)

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

B

C

D

Section 2.4 Assessment

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

A.independent, x

B.independent, y

C.dependent, x

D.dependent, z

Section 2-4B

C

D

Section 2.4 Assessment

What kind of graph shows how quantities vary across categories?

A.pie charts

B.line graphs

C.Venn diagrams

D.bar graphs

Section 2-4Study Guide

Chapter Assessment

Standardized Test Practice

Image Bank

Concepts in Motion

Resources MenuSection 2.1 Units and Measurements

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.

Section 2.2 Scientific Notation and Dimensional Analysis

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.

Section 2.3 Uncertainty in Data

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

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.

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.

B

C

D

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

A.gallon

B.quart

C.m3

D.kilogram

Chapter Assessment 1B

C

D

Divide 6.0 109 by 1.5 103.

A.4.0 106

B.4.5 103

C.4.0 103

D.4.5 106

Chapter Assessment 3B

C

D

Round the following to 3 significant figures 2.3450.

A.2.35

B.2.345

C.2.34

D.2.40

Chapter Assessment 4B

C

D

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

A.x-axis

B.slope

C.y-axis

D.y-intercept

Chapter Assessment 5B

C

D

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

STP 3B

C

D

Which is NOT a quantitative measurement of a liquid?

A.color

B.volume

C.mass

D.density

STP 5IB Menu

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