Exponents

SLIDE SHOW: REAL LIFE APPLICATIONS FOR EXPONENTS media type="custom" key="23922388"

=**What are exponents? Why do we use them? How do we add, subtract, multiply, & divide them?**= SEE THIS LINK: Everything You Ever Wanted to Know About Exponents

=Where do you need or use exponents in everyday life?= Common people who are not using math in their work or anything wouldn't typically use exponents as such in normal life, since it doesn't occur that often that you'd need to calculate 7 x 7 x 7 x 7 or 0.1 x 0.1 x 0.1 x 0.1 x 0.1 or other such calculations. Exponents are more or less just a shorthand notation for multiplying the same number by itself several times - and in normal life you just don't need such often. One example of how exponents do kind of connect with our everyday lives: when we speak about square feet, square meters, square inches, square miles, square kilometers or any other area units, or when we speak about cubic feet, cubic meters, cubic centimeters or any other such volume units. The unit "square foot" is actually 1 foot x 1 foot, or (1 foot) squared, or (1 foot) to the power of 2. Similarly, a cubic foot is 1 foot x 1 foot x 1 foot, or (1 foot) cubed, or (1 foot) to the power of 3. If you talk about SQUARE shaped areas, for example if you say "My room is twelve by twelve square", you're meaning your room is 12 feet x 12 feet, or 122 square feet. Another kind of indirect example is if you talk about extremely tiny or extremely big quantities. For example, the term 'nanometer' means 10-9 meter. The prefix 'nano' means the number 10-9 - an extremely small number. Or, within computer world you often see megabytes, gigabytes, terabytes. "Mega" means 106 or one million, "giga" means 109, and "tera" means 1012. Or megahertz - million hertz.

= = =**More on Uses of Exponents:**=

Scientific Notation

 * Suppose you have a chemical [[image:http://images.intellitxt.com/ast/adTypes/icon1.png link="http://www.ehow.com/list_5814087_use-exponents-real-life.html#"]] 0.000383 grams per liter, or a solar mass of 456,000,000,000,000,000,000 kg. Those zeroes take up a lot of space. Scientific notation simplifies this by writing the last number, for example, as 456x10^18 kg, which means 456 followed by 18 zeroes. Inversely, the chemical concentration is written with a negative sign: 3.83x10^-4. The -4 means that the decimal point is moved to the left four places.

Carpentry

 * In carpentry, surface area is expressed in squared units. So the units have their own exponents. For example, a board that is 10 feet long and 3 inches wide has a surface area on one side of 3/12 feet x 10 feet, or 2.5 ft^2. The 2 is the exponent of the unit “feet,” to indicate that the measurement is in two dimensions (area) instead of one dimension (length).

Compounding Interest

 * [[image:http://images.intellitxt.com/ast/adTypes/icon1.png link="http://www.ehow.com/list_5814087_use-exponents-real-life.html#"]] balances and loans earn interest. Compounded interest is interest that--after an account earns that interest--itself begins earning interest. So if an annual interest rate is 4%, and it earns the interest on a $100 balance for 3 years, an exponent represents the earning of new interest on the old principal for several years: $100x1.04x1.04x1.04 = $100x1.04^3.