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Martin-Gay, Beginning Algebra, 5ed 22 In many fields of science we encounter very large or very small numbers. Scientific notation is a convenient shorthand for expressing these types of numbers. A positive number is written in scientific notation if it is written as a product of a number a, where 1 a < 10, and an integer power r of 10. a 10 r A number between 1 and 10 times a power of ten.

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Martin-Gay, Beginning Algebra, 5ed 33 Write each of the following in scientific notation. 4700 1) Have to move the decimal 3 places to the left, so that the new number has a value between 1 and 10. Since we moved the decimal 3 places, and the original number was > 10, our count is positive 3. 4700 = 4.7 10 3 0.00047 2) Have to move the decimal 4 places to the right, so that the new number has a value between 1 and 10. Since we moved the decimal 4 places, and the original number was < 1, our count is negative 4. 0.00047 = 4.7 10 4 Example:

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Martin-Gay, Beginning Algebra, 5ed 44 Write each of the following in standard notation. 5.2738 10 3 1) Since the exponent is a positive 3, we move the decimal 3 places to the right. 5.2738 10 3 = 5273.8 6.45 10 5 2) Since the exponent is a negative 5, we move the decimal 5 places to the left. 00006.45 10 5 = 0.0000645 Example:

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Martin-Gay, Beginning Algebra, 5ed 55

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77 Multiplying and dividing with numbers written in scientific notation involves using properties of exponents. Perform the following operations. = (7.3 · 8.1) (10 2 · 10 5 ) = 59.13 10 3 (7.3 10 2 )(8.1 10 5 ) a) Example: = ( 5.913 10 1 ) 10 3 = 5.913 10 4

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Martin-Gay, Beginning Algebra, 5ed 88 b)

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Martin-Gay, Beginning Algebra, 5ed 99 Example:

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Martin-Gay, Beginning Algebra, 5ed 10 Example:

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