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§ 9.5

§ 9.5. Scientific Notation. greater than 1 and less than 10. a power of 10. Scientific notation. Scientific Notation. A positive number is in scientific notation if it is in the form a  10 n , where a is a number greater than (or equal to) 1 and less than 10, and n is an integer.

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§ 9.5

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  1. § 9.5 Scientific Notation

  2. greater than 1 and less than 10 a power of 10 Scientific notation Scientific Notation A positive number is in scientific notation if it is in the form a 10n, where a is a number greater than (or equal to) 1 and less than 10, and n is an integer. 5600 = 5.6  1000 = 5.6  103 78,200,000 = 7.82  10000000 = 7.82  107

  3. What power? Ending position of decimal point Starting position of decimal point Standard Notation to Scientific Notation Example: Write 67,300 in scientific notation. 67,300. = 6.73  10 The decimal point was moved 4 places to the left, so we use a power of 4. 67,300 = 6.73  104 A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.

  4. The positive exponent indicates the number of places to move the decimal place to the right. Any number to the zero power is 1. The negative exponent indicates the number of places to move the decimal place to the left. Negative Exponents Notice the following pattern when raising a base of 10 to positive and negative exponents.

  5. What power? Ending position of decimal point Starting position of decimal point Standard Notation to Scientific Notation Example: Write 0.048 in scientific notation. 0.048 = 4.8  10 The decimal point was moved 2 places to the right, so we use a power of –2. 0.048 = 4.8  10–2 A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.

  6. Scientific Notation to Standard Notation Example: Write 9.1  104 in standard notation. 9.1  104 = 9.1000  104 = 91,000 Move the decimal point 4 places to the right. Example: Write 6.72  10–3 in standard notation. 6.72  10–3 = 6.72  10–3 = 0.00672 Move the decimal point 3 places to the left.

  7. 4.52  108 Add the decimal part. Leave the power of 10 unchanged. + 5.63  108 0.842  105 Rewrite 8.42  104 as 0.842 105. – 1.78  105 Adding and Subtracting in Scientific Notation Numbers in scientific notation may be added or subtracted if they have the same power of 10. We add or subtract the decimal part and leave the power of 10 unchanged. Example: Add. 4.52  108 + 5.63  108 10.15  108 Example: Subtract. 8.42  104– 1.78  105 10.15  105

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