To simplify the expression \((3.2 \times 10^{-2})(4.2 \times 10^{6}) \div (5.2 \times 10^{5})\), we will follow these steps:
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Multiply the first two terms: \[ (3.2 \times 4.2) \times (10^{-2} \times 10^{6}) = 13.44 \times 10^{4} \]
Here, \(10^{-2} \times 10^{6} = 10^{(-2+6)} = 10^{4}\).
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Now, divide by the third term: \[ \frac{13.44 \times 10^{4}}{5.2 \times 10^{5}} = \frac{13.44}{5.2} \times \frac{10^{4}}{10^{5}} \]
For the powers of ten: \[ \frac{10^{4}}{10^{5}} = 10^{(4-5)} = 10^{-1} \]
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Now, calculate \(\frac{13.44}{5.2}\): \[ \frac{13.44}{5.2} \approx 2.58 \]
So, we have: \[ 2.58 \times 10^{-1} \]
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Convert to standard notation: \[ 2.58 \times 10^{-1} = 0.258 \]
None of the answer choices correspond exactly, but it seems there was a slight miscalculation earlier. Let's verify:
If we divide 13.44 by 5.2 more carefully: \[ \frac{13.44}{5.2} \approx 2.58 \text{ is correct.} \]
Thus, \(2.58 \times 10^{-1} = 0.258\).
Given the options provided (0.00026, 0.0026, 0.26, 2.6), the closest answer (if we round appropriately) would be 0.26.
So the answer is: \[ \boxed{0.26} \]