Definition: Scientific notation writes a number as a product of a value from 1 up to 10 and a power of 10, making very large or small numbers easy to handle.
What is scientific notation?
It is a compact format: a x 10n, where 1 <= a < 10 and n is an integer.
How do you convert a large number?
Move the decimal point until one nonzero digit is on its left, and count the moves. The distance from the Earth to the Sun is about 93,000,000 miles. Moving the decimal 7 places gives 9.3 x 107.
How do you convert a small number?
Moving right gives a negative exponent. A hair is 0.00007 meters wide. That is 7 x 10-5 meters.
How do you compute with it?
Multiply the front numbers and add exponents. (4 x 103)(6 x 105) = 24 x 108 = 2.4 x 109. Remember to renormalize.
For addition, match the exponents first: 3.2 x 104 + 5 x 103 = 3.2 x 104 + 0.5 x 104 = 3.7 x 104.
What is a common mistake?
Leaving the front number outside the range, like 24 x 108. Also, a negative exponent does not make the number negative.