When dealing with very large or very small numbers, keeping track of place value can be difficult. For this reason, numbers such as these are often expressed in scientific notation.

Scientific Notation A number is expressed in scientific notation when it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than or equal to 10. A number in scientific notation is written as a x 10 n, where 1≤ a < 10 and n is an integer.

The following examples show one way of expressing a number that is written in scientific notation in its decimal or standard notation. Look for a relationship between the power of 10 and the position of the decimal point in the standard notation of the number.

6.59 x 10 4 = 6.59 x 10,000 = 65,900 The decimal place moved 4 places to the right.

4.81 x = 4.81 x = 4.81 x = The decimal point moved 6 places to the left.

These examples suggest the following rule for expressing a number written in standard notation in scientific notation.

Scientific to Standard Notation Use these steps to express a number of the form a x 10 n in standard notation. Determine whether n > 0 or n < 0. If n > 0, move the decimal point in a to the right n places. If n < 0, move the decimal point in a to the left n places. Add zeros, decimal point, and/or commas as needed to indicate place value.

Standard to Scientific Notation Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a. Observe the number of places n and the direction in which you moved the decimal point. If the decimal point moved to the left, write as a x 10 n. If the decimal point moved to the right, write as a x 10 -n.

You will often see large numbers in the media written using a combination of a number and a word, such as 3.2 million. To write this number in standard notation, rewrite the word million as The exponent 6 indicates that the decimal point should be moved 6 places to the right. 3.2 million = 3,200,000

Products and Quotients with Scientific Notation You can use scientific notation to simplify computation with very large and/or very small numbers.