2: Units, Measurement, Graphing, and Calculation
- Page ID
- 121727
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 2.1: Introduction and Learning Objectives
- This page emphasizes the importance of equipping future educators with essential skills in math, measurements, and graphing for effective teaching in physical science. It reviews fundamental math concepts and delves into geometry, error analysis, data interpretation, and dimensional analysis. Mastery of these topics aims to inspire students' understanding of scientific principles while cultivating critical thinking skills for their academic and professional futures.
- 2.2: Math Review
- This page discusses key mathematical concepts such as order of operations, negative numbers, decimals, fractions, and formulas. It covers geometric measures including perimeter, circumference, area, surface area, and volume. The content includes percent calculations, ratios, proportions, and angle measurements, as well as data analysis methods like mean, median, mode, and probability, all aimed at aiding the understanding and evaluation of mathematical expressions and relationships.
- 2.2.1: Order of Operations
- 2.2.2: Negative Numbers
- 2.2.3: Decimals
- 2.2.4: Fractions
- 2.2.5: Formulas
- 2.2.6: Perimeter and Circumference
- 2.2.7: Percents Part 1
- 2.2.8: Ratios, Rates, Proportions
- 2.2.9: Percents Part 2 and Error Analysis
- 2.2.10: Percents Part 3
- 2.2.11: Angles
- 2.2.12: Triangles
- 2.2.13: Area of Polygons and Circles
- 2.2.14: Composite Figures
- 2.2.15: Surface Area of Common Solids
- 2.2.16: Converting Units of Area
- 2.2.17: Volume of Common Solids
- 2.2.18: Area of Regular Polygons
- 2.2.19: Pyramids and Cones
- 2.2.20: Mean, Median, Mode
- 2.2.21: Probability
- 2.2.22: Standard Deviation
- 2.3: Rules of Exponents and Scientific Notation
- In this section, we review the rules of exponents. Recall that if a factor is repeated multiple times, then the product can be written in exponential form xⁿ. The positive integer exponent n indicates the number of times the base x is repeated as a factor.
- 2.4: Calculator skills
- Scientists use all kinds of equipment to measure matter. Balances are used to measure mass while pipettes are used to measure volume. Errors in measurements can be made if the scientist does not know how to properly use the equipment or if the equipment is damaged. It is important that you know the types of equipment a scientists uses and the basic units that are found on the equipment. In addition, memorize and be able to apply the necessary conversion factors for this course.
- 2.5: Precision and GPE
- This page explains precision and accuracy in measurements, crucial for estimating and rounding numbers. Precision relates to the place value of the rightmost significant figure, while accuracy concerns the number of significant figures. It covers rounding methods, the impact of varying precision in addition or subtraction, and the greatest possible measurement error (GPE). Exercises are included to enhance comprehension through practical applications.
- 2.6: Accuracy and Significant Figures
- Every measurement contains some error. A standard sheet of paper is 8.5 inches wide and 11 inches high, but it’s possible that the actual measurements could be closer to 8.4999 and 11.0001 inches. Even if we measure something very carefully, with very sensitive instruments, we should assume that there could be some small measurement error.
- 2.7: Significant Figures - Writing Numbers to Reflect Precision
- Uncertainty exists in all measurements. The degree of uncertainty is affected in part by the quality of the measuring tool. Significant figures give an indication of the certainty of a measurement. Rules allow decisions to be made about how many digits to use in any given situation.
- 2.8: Measurement
- This page emphasizes the significance of expressing quantities with both numbers and units, illustrating its relevance in daily activities and crucial in fields like chemistry. It highlights that units prevent confusion and potential hazards, as numbers alone can be misleading. The text concludes with exercises aimed at reinforcing the understanding of identifying numbers and units in quantities, underscoring their importance for accurate measurement.
- 2.9: Graphing
- This page describes a lab focusing on graphing techniques with Google Sheets, specifically for scatter plots and analyzing the solubility of sodium nitrate at different temperatures. Students will learn to create and interpret graphs, identify trends, and predict measurements using various mathematical models. The text also provides instructions for managing nonlinear data, making calculations, and understanding graph relationships.
- 2.10: End of Chapter Activity
- This page discusses the Next Generation Science Standards (NGSS) for K-12 education, emphasizing Disciplinary Core Ideas, Science and Engineering Practices, and Crosscutting Concepts. The aim is to enhance students' scientific understanding and essential skills for future endeavors. An assignment includes developing a lesson plan for K-2 or 3-5 students that focuses on mass, volume, and length, utilizing hands-on activities and tools such as balance scales and graduated cylinders.
- 2.11: End of Chapter Key Terms
- This page offers a detailed glossary of key terms in measurement, graphing, and calculations, including definitions of crucial concepts like the International System of Units (SI), various measurement types, and principles such as precision and accuracy. It discusses graph types, the Cartesian coordinate system, variable relationships, and highlights significant statistical measures and calibration processes.

