WebQuest: How Big Do Numbers Get?

Why are we doing this?

To put large or small numbers in prospective, we often write them as a product of a number between 1 and 10 and some appropriate power of 10. This makes calculations and approximations easier, but it can make extremely large or small numbers appear deceptively small. 7 × 1021 is actually 7,000,000,000,000,000,000,000 (read "seven sextillion"), which is more than a million times larger than the US national debt.

Technical Stuff:

Scientific Notation is a format in which a number is written as a product of a number between 1 and 10 and some appropriate power of 10. When switching to or from scientific notation, in lieu of trying to memorize which way to move a decimal point, realize the number in scientific notation is equal to the number in standard notation. For example, two write the number 0.000706 in scientific notation, we know the decimal point has to be moved 4 places, indicating the number in scientific notation in either 7.06 × 104 or 7.06 × 10-4. Since it is small (less than 1), the power of 10 cannot be positive, so it must be 7.06 × 10-4. Names of Large Numbers Here is a list of the names for the place value groups of large numbers, with their standard form representations. Number Power of Ten Standard Form   one thousand one million one billion one trillion one quadrillion one quintillion one sextillion one septillion one octillion one nonillion one decillion one undecillion 10^3 10^6 10^9 10^12 10^15 10^18 10^21 10^24 10^27 10^30 10^33 10^36 1,000 1,000,000 1,000,000,000 1,000,000,000,000 1,000,000,000,000,000 1,000,000,000,000,000,000 1,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000,000,000,000 1,000,000,000,000,000,000,000,000,000,000,000,000   A googol is a 1 with a hundred zeroes behind it, or 10100. A googolplex is a 1 with a googol zeroes behind it, or 1010100. There is not enough time in your lifetime to write the standard form of a googolplex. The term order of magnitude is another way to refer to a power of ten, and is often used in expressing an estimation of a very large or small amount.

First, let's do some math.
	Write the following numbers in scientific notation.   a. 600 b. 0.00004056   Answer --> 6 x 10^2 Answer --> 4.056 x 10^-5         c. 0.7 d. 9,120,000,000,000,000   Answer --> 7 x 10^-1 Answer --> 9.12 x 10^15             Write the following numbers in standard notation.   a. 7.06 × 10-1 b. 3.0906 × 103   Answer --> 0.706 Answer --> 3090.6

Now, let's explore a website.

The Scientific Notation Problem Generator allows the user to practice converting to and from scientific notation. The directions provided at the site indicate clicking the New Problem button gives the user either the scientific notation or standard notation representation of a number. You are then to enter the corresponding value(s) in the empty cell(s) and click the Check Answer button. Use the site to work with scientific notation until you are comfortable with the conversion processes. This Big Number Names website expands the table of names from the above section.

Questions to think about.

1. If it took one second to write each zero, how long (in days, hours, minutes and seconds) would it take to write one million zeros?   Answer --> 11 days, 13 hours, 46 minutes, and 40 seconds     2. A light travels approximately six trillion miles a year (called a light year). What is this number written in scientific notation?   Answer --> 6 x 10^12     3. The prefix bi- means two, tri- means three and quad- means four. Why are these prefixes used to represent a billion, trillion, and quadrillion, respectively?   Answer --> A billion is 1000^2, a trillion is 1000^3, and a quadrillion in 1000^4. Thus, the prefixes are used to indicate the power of 1000.     4. How close is a gooloplex to infinity?   Answer --> Not close at all.