To simplify the expression \((3.2 \times 10^{-2})(4.2 \times 10^{6})/(5.2 \times 10^{5})\), we can follow these steps:
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Multiply the numerators: \[ (3.2 \times 10^{-2}) \times (4.2 \times 10^{6}) = (3.2 \times 4.2) \times (10^{-2} \times 10^{6}) \] Calculating \(3.2 \times 4.2\): \[ 3.2 \times 4.2 = 13.44 \] Now for the powers of 10: \[ 10^{-2} \times 10^{6} = 10^{-2 + 6} = 10^{4} \] So, the product becomes: \[ 13.44 \times 10^{4} \]
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Now, divide by the denominator: \[ \frac{13.44 \times 10^{4}}{5.2 \times 10^{5}} = \frac{13.44}{5.2} \times \frac{10^{4}}{10^{5}} \] Calculating \(\frac{13.44}{5.2}\): \[ 13.44 \div 5.2 \approx 2.585 \] Now for the powers of 10: \[ \frac{10^{4}}{10^{5}} = 10^{4-5} = 10^{-1} \]
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Combine the results: \[ 2.585 \times 10^{-1} \] This can be written as: \[ 0.2585 \]
Thus, the value of the expression in standard notation is: \[ \boxed{0.2585} \]
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