4.2: Corequisite- Conversion, Estimation, Percentages and Ratios, Scientific Notation
- Page ID
- 148600
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)SPECIFIC OBJECTIVES
By the end of this lesson, you should understand that
- the magnitude of large numbers is seen in place value and in scientific notation.
- proportions are one way to compare numbers of varying magnitudes.
- different comparisons may be needed to accurately compare two or more quantities.
- estimation is a valuable skill.
- standard benchmarks can be used in estimation.
- there are many strategies for estimating.
- percentages are an important quantitative concept.
By the end of this lesson, you should be able to
- express numbers in scientific notation.
- use multiple computations to compare quantities.
- convert between millions, billions, and trillions.
- compute basic percentages and ratios.
- express one number as a percentage of another.
PROBLEM SITUATION: COMPARING POPULATIONS
In this problem situation, you are going to compare the populations of China and the United States, and you will compare the population of each country to the population of the world. Since the population of each of these countries is very large, you will use scientific notation to write your answers. Recall that scientific notation is a special way of writing very large or very small numbers. A number in scientific notation is written in the form: a × 10n where 1 ≤ a < 10; and n is an integer. An integer, commonly known as a whole number, is a number that can be written without a fractional component. Below are two examples of very large numbers written in scientific notation.
Examples:
- In 2020, the total population of Asia was approximately 4.7 billion people.2 You can write this as 4,700,000,000 or you can use scientific notation to write it as 4.7 × 109 people.
- 28,930,000 can be written in scientific notation as 2.893 × 107.
(1) In late-2022, the population of the United States was 333,000,000.3 In late-2022, Earth’s population was about 7.9 billion. Write these numbers in scientific notation.
(a) U.S. population in scientific notation:
(b) World population in scientific notation:
(2) What are some other ways you could compare the population of the United States to the population of the earth besides writing the two numbers in scientific notation? Think about forms of comparisons using both estimation and calculation.
(3) A ratio is an expression that compares how much there is of one thing to another. Ratios are often written as fractions. In mid-2022, the population of China was 1.412 billion.4 Use a ratio to compare the population of China in 2022 to the population of Earth in 2022 (7.9 billion). Write your answer as a fraction.
(4) Compare China’s population with the population of the United States using a ratio (with the U.S. population as the reference value). Write a sentence that interprets this ratio in the given context.
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2 https://www.prb.org/international/geography/asia/