Special Numbers
A Math World Topic
Exponents
A convenient way to write large numbers is by using exponential notation. The number 53 means 5 X 5 X 5. To make it easier to show on a keyboard, the symbol 5^3 can also be used. As an example, 5300 can be expressed as 53 X 103. One quadrillion (1,000,000,000,000,000) can be written as 10^15 or 1015
There are also negative exponents. 5^-3 5-3 means 1/(5^3). Exponents can get very complicated in formulas which can be found in advanced math textbooks. 
Roots
An root is exactly the opposite of an exponent. The square root of a number is a number multiplied by itself equals that number. A square root is always positive. The square root of – 4 is undefined. The following are the first ten square roots that come out even: 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.
The cube root of a number is a number when multiplied by itself three times equals that number. The cubed root of 8 is 2 because 2 X 2 X 2 = 8. A negative cubed root is always a negative answer. The first ten cubed root that come out even 1, 8, 27, 64, 125, 216, 343, 729, 1000.
The fourth root of a number means what four numbers multiplied together will equal the number. The fourth root of 16 is 2, because 2 X 2 X X 2=8
Factorials
Factorials are used for probability and statistics. It is written with an “!”, 4! means 4 X 3 X 2 X 1 or 24. 5! is 5 x 4 X 3 X 2 X 1 or 120. As you can see, factorials can get really large, really fast. However, both 0! and 1! are equal to 1.
Mr. Wood is playing group chess and there are ten people on his team. In making the team order, how many different combinations are there. Is is a factorial permutation problem. Permutations are an arrangement of a list in a specific order. The answer to this problem is10! or 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. So the there are 420,320 possibilities.
Other Symbols
Absolute Value is used in geometry as the positive distance between to points. It is always positive. So the absolute value of -6 is 6. It is shown as |-6| The absolute value of 6 is also 6. So the |5|=5 |-5| =5.
Undefined: ( ) If a problem does not have an answer, it is considered undefined. It can be written as the following: { } or 0 with a line through it or a backslash
Micron: µ – A micron is used in high tech microscopic work. 1000 microns is a millimeter.
Infinity: ∞ A symbol that means any number is correct.
Large Numbers and the Undecillion Caterpillar
Large Numbers are a great way to motivate young students when exposed to advanced concepts. This third-grade activity involves using egg cartons to make a caterpillar. The various egg compartments are used for place value. Students can build this project by supplying three egg cartons. Some classes make a huge googol caterpillar on a math day celebration.
Pi (π)
Pi is a special number used in geometry for figuring out areas of circles. Pi is a special decimal number that is not finite, and does not repeat, yet it is infinite. The fraction for Pi is 22/7. The decimal for Pi carried out to 63 places is 3.14159265358979323846264338327950288419716939937510582097494459230
Hex Codes
Special six-digit codes based on the hexadecimal number system in order to identify colors. There are a few basic codes for simple numbers that may be seen in websites. White= FFFFFF BLACK= 000000 BLUE = 0000FF YELLOW= FFFF00 RED= FF0000 GREEN= 008000