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Scientific Notation

Concept

Scientific Notation

Scientific notation is a compact way of writing very large or very small numbers. A number written in scientific notation follows the form where and is an integer. For example, the number million can be rewritten as the product of and a multiple of Then, the multiple of is rewritten as a base power. Scientific notation can also be applied to very small decimal numbers, where there are many zeros before the significant digits, such as In such cases, numbers are rewritten as a division by a multiple of Division by a multiple of is equivalent to multiplication by a base power with negative exponent. Below are a few more examples of numbers written in scientific notation.

Decimal Form Write as a product or division Scientific Notation

An intuitive way to rewrite a number greater than in scientific notation is done by counting the number of places the decimal needs to move so the number is greater than or equal to and less than The number of places the decimal moved from right to left indicates the exponent to be used for the base power.

Similarly, for numbers less than such as the decimal will move from left to right. In this case, the number of places moved indicates the negative exponent to be used for the base power.