Exploring Our Universe:
From the Classroom to Outer Space
I. Spectroscopy
Student Activity #1-part 1

1. IS THERE A GOOGOL OF ANYTHING?

If someone asks you, "what's the biggest number you can think of," what comes to mind? Back in the 1940s, American mathematician Edward Kasner was asking himself the same question. He decided to ask his nine year-old nephew what he would name a really big number. His nephew's answer was, "a googol!"

What is a googol? Kasner defined a googol to be a one followed by one hundred zeros:

10,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000

As you can see, a googol is not an easy number to write out! To express very large numbers in an easy form, people use scientific notation (the product of a decimal with only one whole number place value- the ones place- multiplied by a power of ten):

a googol = 1 x 10^100
= 10^100
(since 1 times any number equals that number)

To write other large numbers in scientific notation, count the number of place values behind the largest place value, then write the product of a decimal times ten raised to the power equal to the number of place values you counted:

Example:

The speed of light = 299,800,000 meters/second = 2.998 x 10^8m/s

For very small numbers, count the number of decimal places from the decimal point down to and including the largest significant digit, then write a product of a decimal times ten raised to the negative power equal to the number of place values you counted:

Example:

The diameter of an atom = 0.000000011 centimeters = 1.1 x 10^-8cm

NOTE: If there is only one significant digit, then your answer will be the product of a whole number times a power of ten (i.e. 5000 = 5 x 10³, or .0004 = 4 x 10^-4).

PRACTICE PROBLEMS (Write each number using scientific notation.)

  1. 1 mile (mi) = 1609 meters (m) = ___________

  2. 1 kilometer (km) = 1,000,000 millimeters (mm) = ___________

  3. 1 inch (in) = 0.0254 m = ___________

  4. 1 microgram (mu;g) = 0.000001 gram (g) = ____________

  5. The distance from the Earth to the Moon =238,900 mi = ____________

  6. The radius of a hydrogen atom = 0.00000000005 m = ____________

  7. The distance from the Earth to the Sun = 150 million km = __________

  8. One light-year (ly) = 5,880,000,000,000 mi = ____________

  9. The mass of one hydrogen atom = 0.000000000000000000000000005 kg = ____________

  10. The mass of the Earth = 5,976,000,000,000,000,000,000,000 kg = ____________

Extension Activities:

If you would like to read more about a googol, googolplex and other really big numbers, visit the following website on the Internet:

http://public.logica.com/~stepneys/cyc/g/googol.htm