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Scientific Notation

Writing and reading scientific notation

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Big and Small

Big and Small

Credit: The National Guard
Source: http://commons.wikimedia.org/wiki/File:New_Jersey_National_Guard_-_Flickr_-_The_National_Guard_(65).jpg
License: CC BY-NC 3.0

In October, 2012, Hurricane Sandy devastated several Atlantic seaboard states in the U.S. The total cost of the storm is hard to estimate, but it’s probably at least $65,000,000,000. That’s 65 billion dollars! There’s no doubt that natural disasters are expensive. The numbers of dollars they cost are usually very big numbers.

Why It Matters

  • It’s easier to read and write very big or very small numbers using scientific notation. For example, the $65,000,000,000 cost of Hurricane Sandy is written in scientific notation as \begin{align*}\$6.5 \times 10^{10}\end{align*}.
  • Why is scientific notation important? You’re less likely to make mistakes reading or writing very big and very small numbers if you use scientific notation. It also makes it much easier to tell at a glance which numbers are bigger or smaller without counting long strings of zeros.
  • Credit: Jonathan Combe
    Source: http://www.flickr.com/photos/jono566/9494802016/
    License: CC BY-NC 3.0

    Scientific notation is useful for measuring large distances, such as the distance between stars[Figure2]

  • Watch this clever rap to see how to read and write numbers in scientific notation: http://www.youtube.com/watch?v=HtXTKrigYqk

Can You Apply It?

Learn more about scientific notation at the link below. Then answer the questions that follow.

  1. Outline the steps used to express a big number such as 65 billion in scientific notation.
  2. How do you convert a small number to scientific notation?
  3. A lab technician counts red blood cells in a smear of a patient’s blood on a microscope slide. From this number, she will estimate the number of red blood cells in a microliter of the patient’s blood. The normal number is about 5,000,000 red blood cells per microliter. What is this number in scientific notation?
  4. A single red blood cell is about 0.000007 meters in diameter. How would you write this number in scientific notation?
  5. Pollen grains cause allergies in many people, but they usually are too small to see. A grain of ragweed pollen, for example, is only 0.00002 meters in diameter. How is this number written in scientific notation?
  6. Viruses are another common cause of human illness. They are even smaller than pollen grains. A typical virus is only about 0.00000002 meters in diameter. Express this number in scientific notation.

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Image Attributions

  1. [1]^ Credit: The National Guard; Source: http://commons.wikimedia.org/wiki/File:New_Jersey_National_Guard_-_Flickr_-_The_National_Guard_(65).jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Jonathan Combe; Source: http://www.flickr.com/photos/jono566/9494802016/; License: CC BY-NC 3.0

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