Skip to main content
Mathematics LibreTexts

1.4.3.1: Exercises

  • Page ID
    82930
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Section 1.4.4.1 Exercises

    1. Change from standard notation to scientific notation.
      1. 492,000
      2. 23,487,000,000,000
      3. 0.000098
      4. 0.00000000000938
      5. Change from scientific notation to standard notation.
        1. \(6.32 \times 10^5\)
        2. \(8.3 \times 10^{13}\)
        3. \(5.26 \times 10^{-3}\)
        4. \(8.265 \times 10^{-8}\)
      6. Multiply or divide the numbers in scientific form.  Leave the answer in scientific form.
        1. \( (3.7 \times 10^8)(1.5 \times 10^3) \)
        2. \( (4.2 \times 10^4)(6.8 \times 10^{-7})\)
        3. \( (3.7 \times 10^8)\div(1.5 \times 10^3)  \)
        4. \((4.2 \times 10^4)\div(6.8 \times 10^{-7})\)
        5. \( \dfrac{(6\times 10^7)(4.8\times10^{-6})}{2.4\times 10^5}\)
      7. If the U.S. annual production of sugar is 9 million tons, estimate the number of grains of sugar produced in a year in the U.S.  Use scientific notation.  (Note:  There are 2,000 lbs per ton; assume there are 2,260,000 grains in a pound of sugar.)
      8. The national debt in 2020 was approximately $26.7 trillion.  Write this number in scientific notation.  Suppose, also, that in 2020 there were about 331,500,000 people in the U.S.  If the debt is divided equally among these people, how much is each person’s share?
      9. For the next few problems, you will need the following information.
        One astronomical unit (AU) is the average distance of the earth from the sun, or approximately 93,000,000 miles.
        Jupiter’s average distance from the sun is 5.2 AU.
        The time it takes an object moving at a constant speed is given by the formula \(t = \dfrac{d}{r}\), where \(d\) represents distance traveled, \(r\) represents speed of the object, and \(t\) represents time the object is in motion.
        1. Write the distance of the earth from the sun in scientific form.
        2. What is Jupiter’s average distance from the sun in miles?  Do the computation in both standard form and scientific form.  Which is easier?
        3. How long does it take light from the sun to reach earth?  How many minutes is this?
        4. How far will light travel in one year?

    This page titled 1.4.3.1: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia.

    • Was this article helpful?