Scientific notation makes large numbers more manageable. Scientific notation has two parts, as Karen Timberlake describes in "Structures of Life: General, Organic, and Biological Chemistry," which consists of the coefficient and a power of 10. The coefficient is number 1 through 9 which is multiplied by a power of 10.
Recognizing Scientific Notation
Scientific notation is usually expressed in a form similar to: 5.2x10^4 which is short hand for 52,000
However, in many calculators and computer software you will see scientific notation written with an "E". Timberlake describes this by saying, scientific notation "s usually shown in the display as a number from 1 to 9 followed by a space and the power of 10." Insert x10^ in place of the "E" and use the power of 10 as the exponent.
For example you might see 5.2E4 in a calculator, which is the same as 5.2x10^4
Converting Scientific Notation to a Standard Number
If the power of 10 is positive, move the decimal to the right. If the power of 10 is negative move the decimal backwards to the left. E10 means move the decimal to the right 10 places.
If the number 1-9 is a whole number, then the decimal may not be seen, but for the purposes of moving the decimal, there is an invisible decimal after each whole number.
Examples of Converting to Standard Numbers
If your number is 5E10, or 5x10^10, you will move the decimal 10 places to the right and the number will be 50,000,000,000. Scientific notation is shorthand for these long numbers to make them more manageable. A helpful tip when you're dealing with a whole number, such as 5E10, or 5x10^10, is that you can just write the number 5 and simply attach ten "0"s to the end. Yielding 50,000,000,000.
If your number is 5.2E-5, or 5.2x10^-5, you will move the decimal 5 places to the left and the number will be .000052
Converting a Standard Number into Scientific Notation
Converting a large number into scientific notation can be helpful when using extremely large numbers. If you were talking about 125,000,000,000 people it would be useful to write it in scientific notation.
Find the coefficient, a number between 1-9.
In this case, our coefficient is 1.25
Add the power of 10. Count the number of decimal places the decimal has moved, in this case it is 11.
1.25x10^11 is the same as 125,000,000,000 or 1.25E11 in a calculator.
Uses of Scientific Notation
Dealing with numbers that are excessively large or small can be daunting but by simplifying the numbers they become more manageable.
For instance if you are talking about the number of hairs on your head you would have a very large number, and similarly if you were talking about the diameter of one strand of hair it would be too small to discuss in standard numbers.
Uses of scientific notation include math as well as science. Many statisticians and chemists uses scientific notation on a daily basis.