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Scientific Notation: Adding and Subtracting 1. Exponents must be the same or the operation cannot be performed. If the exponents do not agree, change the decimal and the power of ten notation of either number so as to agree with the other. 2. Add or subtract the number. 3. Keep the same power of ten. Examples: 4.2 x 103 = 420 x 101 1 + 2 x 10 = 2 x 101 (CANNOT DO) 422 x 101 = 4.2 x103 (Use correct scientific notation and also use the correct number of significant figures.) 3.3 x 101 = 3.3 x 101 -1 - 7.23 x 10 = 0.0723 x 101 (CANNOT DO) 3.2277 x 101 = 3.2 x 101 Scientific Notation: Multiplying and Dividing MULTIPLICATION: 1. Multiply the numbers. 2. Add the exponents for the power of ten. Example: (3.0201 x 102)(2.0 x 101) = 6.0 x 103 (Use correct number of significant figures. Use correct scientific notation.) Note: If a power of ten is not expressed, it is understood to be 100, which equals 1. Thus, 4.0 is understood to be 4.0 x 100. DIVISION: 1. Divide the numbers as in any division problem. 2. Subtract the denominator power of ten exponent from the numerator power of ten exponent. Example: 6.0830 x 104 = 3.52 x 102 1.73 x 102 (Use correct number of significant figures. Use correct scientific notation).