1. Scientific Notation A Pithy Guide to Writing LARGE and small numbers using it… Scientific notation makes calculating distances between stars much easier for astronomers!

2. Scientific Notation Always has the form of a x 10 n Where: 1 < a < 10 OR -10 < a < -1 and n is an integer. In other words, the number is written as a number with one non-zero digit to the left of the decimal point multiplied by a power of 10. The number of digits after the decimal point in a depends on the degree of precision you want to show. Examples: -2.4 x 10 5 9.45 x 10 -3 - 4 x 10 -3

3. Examples of Numbers in Scientific and Standard Notation Scientific Notation: 3.4 x 10 3 2.8 x 10 -5 9.0 x 10 3 -2.4 x 10 7 3.5 x 10 -12 Standard Notation: 3 400.0 0.000 028 9 000.0 -24 000 000.0 0.000 000 000 003 5 Notice that the numbers before the decimals in this column are all between 1 and 10?

4. So how does one translate from standard notation into scientific notation? Let’s find out!

5. Translating from Standard Notation to Scientific Notation: Example 1: Positive Exponents 4 000 000 00.. The decimal moved 6 places to the left. In scientific notation, this would be written: 4.0 x 10 6 123456 To remember which way to move the decimal (left or right), remember that positive exponents (like 6 in the example), give numbers bigger than one.

6. 0 000 000 8 0.. The decimal moved 7 places to the right. In scientific notation, this would be written: 8.0 x 10 -7 123456 To remember which way to move the decimal (left or right), remember that negative exponents (like -7 in the example above) represent very small numbers - numbers that are less than one. As a result, they will always start with zero. 7 Translating from Standard Notation to Scientific Notation – Example 2: Negative Exponents

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