The exponent theorems provide a compact method of writing very large or very small numbers. The method is called scientific notation. A number written in scientific notation has the form `a*10^n`, where `n` is an integer and `1 <= a < 10`. The following procedure is used to change a number from its decimal form to scientific notation.

For numbers greater than `10`, move the decimal point to the position to the right of the first digit. The exponent `n` will equal the number of places the decimal point has been moved. For example,

`7\underbrace{,430,000}_\text{6 places}=7.43 xx 10^6`
For numbers less than `1`, move the decimal point to the position to the right of the first nonzero digit. The exponent `n` will be negative, and its absolute value will equal the number of places the decimal point has been moved. For example,
`0\underbrace{.0000007}_\text{7 places}8=7.8 xx 10^(-7)`

To change a number from scientific notation to its decimal form, reverse the procedure. That is, if the exponent is positive, move the decimal point to the right the same number of places as the exponent. For example,

`3.5 xx 10^5=3\underbrace{50,000}_\text{5 places}`
If the exponent is negative, move the decimal point to the left the same number of places as the absolute value of the exponent. For example,
`2.51 xx 10^(-8)=0\underbrace{.00000002}_\text{8 places}51`

Most scientific calculators display very large and very small numbers in scientific notation. The number `450,000^2` is displayed as `2.025 \ \ \ \ \ 11` or as `2.025`E`11`. This means `450,000^2=2.025 xx 10^11`.