Expressing numbers
Standard notation is the straightforward expression of a number. Numbers such as 17, 101.5, and 0.00446 are expressed in standard notation. For relatively small numbers, standard notation is fine. However, for very large numbers, such as 306,000,000, or for very small numbers, such as 0.000000419, standard notation can be cumbersome because of the number of zeros needed to place nonzero numbers in the proper position.
Scientific notation is an expression of a number using powers of 10. Powers of 10 are used to express numbers that have many zeros:
10^{0}  = 1 
10^{1}  = 10 
10^{2}  = 100 = 10 x 10 
10^{3}  = 1,000 = 10 x 10 x 10 
10^{4}  = 1,000 = 10 x 10 x 10 x 10 
and so forth. The raised number to the right of the 10 indicating the number of factors of 10 in the original number is the exponent. Scientific notation is sometimes called exponential notation. The exponent’s value is equal to the number of zeros in the number expressed in standard notation. Small numbers can also be expressed in scientific notation but with negative exponents:
10^{1}  = 0.1 = 1/10 
10^{2}  = 0.01 = 1/100 
10^{3}  = 0.001 = 1/1,000 
10^{4}  = 0.0001 = 1/1,0000 
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