Math Exponents . . . "why" exponents are used in mathematics is explained using everyday examples . . .

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Math Exponents
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Why exponent notation is used

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Math Exponents - Why Use Exponent Notation? - Introduction to Exponents : An exponent is a shorthand notation which tells how many times a number (or expression) is multiplied by itself.

For example, the number 2 raised to the 3^rd power means that the number two is multiplied by itself three times:

$exponent - 2 raised to the 3rd power - Math$

$base and exponent - Math$

The two in the expression is called the base, and the 3 is called the exponent (or power).

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Do you actually need to use math exponents?

The answer is no. People didn't begin to use exponents until a few hundred years ago.

It is OK to multiply out the numbers and use the result. That is what people did until exponents were invented.

In the example shown above, $exponent - 2 raised to the 3rd power - Math$ . You can just use the 8 rather than 2³ if you wish.

So what is the point of using math exponents?

The primary reason for using exponents is because exponents are shorthand notations which allow us to deal with extremely large and extremely small numbers more easily than using the standard form of a number. In addition, fractional exponents simplify calculations involving radicals.

Exponents make the following common applications possible:

Scientific Notation
(represents large and small numbers as exponents of 10

You can use an interactive Scientific Notation calculator on-line http://freeonlinecalculator.net/calculators/math/scientificnotation.php )

Engineering Notation
(forces different numbers to have exactly the same exponents for comparison purposes eg: lists all numbers as millions, or thousands, etc.)

Logarithms
(logarithms are exponents

You can use an interactive Logarithms calculator on-line http://www.1728.org/logrithm.htm )

Slide rules
(slide rules multiply and divide numbers by adding and subtracting exponents

You can use an interactive slide rule on-line - use the FireFox browser to display properly (FireFox can be downloaded at no charge at: http://en-us.www.mozilla.com/en-US/firefox/) http://www.taswegian.com/TwoHeaded/UniVirtual/UniVirtual.html )

The Richter Scale for measuring the magnitude of earthquakes (The Richter Scale is a scale of exponents. An increase of magnitude of 1 on the Richter Scale means the magnitude of an earthquake has increased 10 times.

You can use an interactive Richter Scale calculator on-line http://home.att.net/~srschmitt/script_earthquake.html )

The Decibel Scale for measuring the relative magnitude of two sounds (The Decibel Scale is a scale of exponents. An increase of 3 decibels is a doubling in the intensity of sound. An increase of 10 decibels is an increase of 10 times the intensity of sound.

You can use an interactive Decibel Scale calculator on-line http://www.daycounter.com/Calculators/Decibels-Calculator.phtml )

Why use exponents? Exponents make many calculations fast and easy. But again, you can use the standard form of a number if you wish - and forget all about exponents.

For example:

Multiply the following two numbers together:

5¹⁰* 5⁶

Finding the result without using exponents is time consuming and tedious:

5¹⁰ = 5*5*5*5*5*5*5*5*5*5

= 9,765,625

5⁶ = 5*5*5*5*5*5

= 15,625

9,765,625*15,625 = 152,587,890,625 (final answer)

Note: if you have tried to multiply the two numbers shown above, you know that most calculators are not accurate when computing numbers beyond 8 or 10 digits (the numbers are automatically rounded by the calculator). However, you can download an excellent precision calculator which can handle thousands of digits for free at http://www.karenware.com/powertools/ptcalc.asp

Finding the result using exponents is fast and easy:

5¹⁰ * 5⁶ = 5¹⁰⁺⁶

= 5¹⁶ (final answer)

Math Exponents: impact your day-to-day finances

Although most people may not stop to think about it, exponents impact most routine financial transactions, either directly or indirectly. Banks, credit unions, the government, car dealerships, and other businesses use exponents to calculate interest and penalties.

For example:

When you deposit money in a bank, the bank will use exponents to calculate how much interest you account has earned. If the bank will pay you compound monthly interest on your deposit, the formula used is:

Total $ in Your Account = (Original Deposit)(1+r)^(m)

r = monthly interest rate entered as a decimal (eg - 1% interest per month would be entered as 0.01); the exponent, m = number of months money is left in the account

If you deposit $100 in an account which pays 1% compounded interest per month, and leave your money in the account for 14 months, your balance can be calculated as:

Total $ in Your Account = ($100 Deposit)(1+0.01)⁽¹⁴⁾

= $114.95

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Math Exponents
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Why exponent notation is used

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Math Exponents . . . Why exponent notation is used

Math Exponents
. . .
Why exponent notation is used