Scientific notation is used to express very large or very small numbers.
A number in scientific notation is written as the product of a number (integer or
decimal) and a power of 10. This number is always 1 or more and less than 10.
For example, there are approximately 6,000,000,000 humans on earth. This number
could be written in scientific notation as 6x109. The number 6,000,000,000
is equivalent to 6*1,000,000,000. The number 1,000,000,000 is equivalent to 109
or 10*10*10*10*10*10*10*10*10.
A number can be converted to scientific notation by increasing the power of ten
by one for each place the decimal point is moved to the left. In the example above,
the decimal point was moved 9 places to the left to form a number more than 1 and
less than 10.
Scientific notation numbers may be written in different forms. The number
6x109 could also be written as 6e+9. The +9 indicates that the
decimal point would be moved 9 places to the right to write the number in standard
form.
Comparing
Two numbers written in scientific notation can be compared. The number with the
larger power of 10 is greater than the number with the smaller power of 10. If the
powers of ten are the same then the number with the larger factor is the larger number.
For example, 3.4x107 is greater than 3.4x104. The number
3.4x107 is greater than 3.1x107.
Numbers written in standard form can be compared to numbers written in scientific
notation by converting one number to a different format so that both are in the same
format.
For example, to compare 3.4x107 and 4,500,000 convert 3.4x107
to 34,000,000 or convert 4,500,000 to 4.5x106 before comparing them.