Amsco Integrated Algebra I: Scientific Notation
 This is a free lesson from our course in Amsco's Integrated Algebra

 This lesson explains basic concepts of how to write numbers into scientific notation and also scientific notation into normal decimal form. In order to write and compute with very large or very small numbers easily, the scientists or mathematicians use scientific notation. If a number is written as the product of two quantities: say the first is a number greater than or equal to 1 but less than 10, and the second is a power of 10, it is stated as expressed in scientific notation. Thus a number is in scientific notation if it is written as a x 10n, where 1 ≤ a < 10 and n is an integer. (More text below video...)
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 (Continued from above) E.g. the distance from the earth to the sun approximately 93,000,000 miles, can be expressed in scientific notation 9.3 * 107. Simply saying numbers in scientific notation look like the example: 4.16 x 10+a and 4.16 x 10-a , where a is always a positive, real number. The 10+a tells us that the decimal point is a places to the right of where it is shown. The 10-a tells us that the decimal point is a places to the left of where it is shown. For example: If you are to write .000331 x 10-8 in scientific notation, follow the steps below: • write the first term, .000331 in scientific notation, which is 3.31 x 10-4 x 10-8 • combine the last two terms using the product rule for exponents. • you’ll get the answer (3.31 x 10-12). In cases of changing from scientific notation to ordinary decimal notation, it can be done by expanding the power of 10 and then multiplying the result by the number between 1 and 10. For example: if the population of a country is 3.75 x 107, the approximate number of people in the country can be worked quickly by moving the decimal point in 3.75 seven places to the right i.e. the final answer is 37,50,0000. The video above will explain in detail with the help of several examples.

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