5.6 Rules of Exponents and Scientific Notation 269 To convert from a number given in scientific notation to decimal notation, we reverse the procedure. TO CHANGE A NUMBER IN SCIENTIFIC NOTATION TO DECIMAL NOTATION 1. Observe the exponent on the 10. 2. a) If the exponent is positive, move the decimal point in the number to the right the same number of places as the exponent. Adding zeros to the number might be necessary. b) If the exponent is negative, move the decimal point in the number to the left the same number of places as the exponent. Adding zeros might be necessary. PROCEDURE Example 7 Converting from Scientific Notation to Decimal Notation Write each number in decimal notation. a) The average distance from Mars to the sun is about × 1.4 108 miles. b) The half-life of uranium-235 is about × 4.5 10 years. 9 c) The average grain size in siltstone is about × − 1.3510 inch. 3 d) A millimicron is a unit of measure used for very small distances. One millimicron is about × − 3.9410 inch. 8 Solution a) × = 1.4 10 140,000,000 8 b) × = 4.5 10 4,500,000,000 9 c) × = − 1.35 10 0.00135 3 d) × = − 3.94 10 0.0000000394 8 7 Now try Exercise 33 Scientific Notation In scientific journals and books, we occasionally see numbers like 1015 and 10 .6− We interpret these numbers as ×1 1015 and 1 10 ,6 × − respectively, when converting the numbers to decimal form. Example 8 Multiplying Numbers in Scientific Notation Multiply × × − (2.1 10 )(9 10 ). 5 3 Write the answer in scientific notation and in decimal notation. Solution We begin by rewriting the product so that 2.1 and 9 are multiplied together and the powers of 10 are multiplied together. × × = × × = × = × = × = − − + − (2.1 10 )(9 10 ) (2.1 9)(10 10 ) 18.9 10 18.9 10 1.89 10 1890 5 3 5 3 5 ( 3) 2 3 Now try Exercise 41 Scientific notation Decimal notation 7 Example 9 Dividing Numbers Using Scientific Notation Divide 0.000000000048 24,000,000,000 . Write the answer in scientific notation.
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