Introduction to Scientific Notation
In applied mathematics, very large and very small numbers are written in compact form by using integer powers of . For instance, the speed of light in vacuum, meters per second (approximately), can be written more compactly as meter per second.
More generally, a real number is said to be expressed in scientific notation if it is written in the form ,
Where is an integer and is a number greater than or equal to , but less than . The integer is called the characteristic of , the number is called the mantissa of , and factor is called the order of magnitude of .
To change a number from ordinary decimal form to scientific notation, move the decimal point to obtain a number between and (one digit in front of the decimal point) and multiply by or by, where is the number of places the decimal points was moved to the left or to the right, respectively. Final zeros after the decimal point can be dropped unless it is necessary to retain them to indicate the accuracy of an approximation.
Example:
Rewrite each statement so that all numbers are expressed in scientific notation.

The volume of the earth is approximately cubic meters.

The earth rotates about its axis with an angular speed of approximately degree per second.
Solution:
(a) We move the decimal point places to the left
to obtain a number between and and multiply by , so that .
Thus, the volume of the earth is approximately cubic meters.
(b) We move the decimal point three places to the right to obtain a number between and and multiply by , so that .
Thus, the earth rotates about its axis with an angular speed of approximately degree per second.
Example:
Rewrite the following numbers in ordinary decimal form.
(a) (b)
Solution:
(a)
(b)
(Very small numbers, written in ordinary decimal form, are easier to read if commas are used to set off zeros in groups of three.)
Names and Scientific prefixes for some integer powers of are listed in table.
Power of 
Names 
Prefix 

Ten 
Deka 

Hundred 
Hecto 

Thousand 
Kilo 

Million 
Mega 

Billion 
Giga 

Trillion 
Tera 

Quadrillion 
Peta 

Tenth 
Deci 

Hundredth 
Centi 

Thousandth 
Milli 

Millionth 
Micro 

Billionth 
Nano 

Trillionth 
Pico 

Quadrillionth 
Femto 