675ed2db-5543-4e55-83a8-5b6ad5882ad9.html

<h4>Applying Scientific Notation</h4>
<p>Let&rsquo;s look at how to solve a real-world problem involving scientific notation.</p>
<p>The specimens below are measured lengths of different tiny animals. Arrange them in order from shortest to longest.</p>

<table class="os-raise-midsizetable">
  <thead>
    <tr>
      <th scope="col">Specimen</th>
      <th scope="col">Length (m)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        A
      </td>
      <td>
        \(7.0\times10^{-3}\)
      </td>
    </tr>
    <tr>
      <td>
        B
      </td>
      <td>
      0.0000847
      </td>
    </tr>
    <tr>
      <td>
       C
      </td>
      <td>
       0.00022
      </td>
    </tr>
    <tr>
      <td>
       D
      </td>
      <td>
     \(1.8\times10^{-4}\)
      </td>
    </tr>
    <tr>
      <td>
       E
      </td>
      <td>
        \(8.92\times10^{-3}\)
      </td>
    </tr>
    <tr>
      <td>
        F
      </td>
      <td>
        \(6.03\times10^{-2}\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<p>To solve this problem, we can convert all of the measurements to decimal form or standard form.</p>
<p>Let&rsquo;s convert all measurements to decimal form from scientific notation.</p>

<table class="os-raise-midsizetable">
  <thead>
    <tr>
      <th scope="col">Specimen</th>
      <th scope="col">Length (m)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
       A
      </td>
      <td>
        \(7.0\times10^{-3} = 0.007\)
      </td>
    </tr>
    <tr>
      <td>
       B
      </td>
      <td>
         0.0000847
      </td>
    </tr>
    <tr>
      <td>
     C
      </td>
      <td>
         0.00022
      </td>
    </tr>
    <tr>
      <td>
      D
      </td>
      <td>
         \(1.8\times10^{-4} = 0.00018\)
      </td>
    </tr>
    <tr>
      <td>
      E
      </td>
      <td>
        \(8.92\times10^{-3} = 0.00892\)
      </td>
    </tr>
    <tr>
      <td>
       F
      </td>
      <td>
     \(6.03\times10^{-2} = 0.0603\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<p>We can now arrange the decimal values in order from shortest to longest:</p>
<p>B, D, C, A, E, F</p>
<p>Let&rsquo;s convert each length into scientific notation and check our answer.</p>

<table class="os-raise-midsizetable">
  <thead>
    <tr>
      <th scope="col">Specimen</th>
      <th scope="col">Length (m)</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>
        A
      </td>
      <td>
        \(7.0\times10^{-3}\)
      </td>
    </tr>
    <tr>
      <td>
       B
      </td>
      <td>
      \(0.0000847 = 8.47\times 10^{-5}\)
      </td>
    </tr>
    <tr>
      <td>
       C
      </td>
      <td>
       \(0.00022 = 2.2 \times 10^{-4}\)
      </td>
    </tr>
    <tr>
      <td>
       D
      </td>
      <td>
       \(1.8\times10^{-4}\)
      </td>
    </tr>
    <tr>
      <td>
        E
      </td>
      <td>
       \(8.92\times10^{-3}\)
      </td>
    </tr>
    <tr>
      <td>
        F
      </td>
      <td>
        \(6.03\times10^{-2}\)
      </td>
    </tr>
  </tbody>
</table>
<br>
<p>The negative exponent with the largest absolute value represents the smallest number, so B is the shortest length.</p>
<p>The negative exponent with the smallest absolute value represents the largest number, so F is the longest length.</p>
<p>When the exponents are equal, compare the decimal part of the number.</p>
<p>The order B, D, C, A, E, F is correct from shortest to longest length.</p>
<h4>Try It: Applying Scientific Notation</h4>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <p>The measurements in the table are sample wavelengths for the given types of waves. Arrange them in order from shortest to longest.</p>
 
    <table class="os-raise-midsizetable">
      <thead>
        <tr>
          <th scope="col">Color</th>
          <th scope="col">Wavelength (m)</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <td>
            red light
          </td>
          <td>
            \(7.0\times10^{-7}\)
          </td>
        </tr>
        <tr>
          <td>
            blue light
          </td>
          <td>
           0.00000045
          </td>
        </tr>
        <tr>
          <td>
           infrared light
          </td>
          <td>
          \(5.0\times10^{-4}\)
          </td>
        </tr>
        <tr>
          <td>
           ultraviolet light
          </td>
          <td>
            \(2.0\times10^{-9}\)
          </td>
        </tr>
        <tr>
          <td>
           microwaves
          </td>
          <td>
           \(1.5\times10^{-1}\)
          </td>
        </tr>
        <tr>
          <td>
            radio waves
          </td>
          <td>
           2.1
          </td>
        </tr>
      </tbody>
    </table>
    <br>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer, then select the <strong>solution</strong> button to compare your work. </p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Compare your answers:</p>
  <p>Here is how to arrange the measurements from shortest to longest:</p>
  <p>Let&rsquo;s convert the values for blue light and radio waves into scientific notation to compare all the values.</p>
  <p>blue light = \(0.00000045 = 4.5\times 10^{-7}\)</p>
  <p>radio waves = \(2.1 = 2.1\times 10^0\)</p>
  <p>So, from shortest to longest the wavelengths are:</p>
  <p>ultraviolet light, \(2.0\times10^{-9}\)<br>
    blue light, \(4.5\times10^{-7}\) <br>
    red light, \(7.0\times10^{-7}\)<br>
    infrared light, \(5.0\times10^{-4}\) <br>microwaves, \(1.5\times10^{-1}\) <br>
    radio waves, \(2.1\times10^0\) </p>
</div>