To simplify the expression \( 0.0002 \div (4 \times 10^{-3}) \), we can start by rewriting \( 0.0002 \) in scientific notation.
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Convert \( 0.0002 \) to scientific notation: \[ 0.0002 = 2 \times 10^{-4} \]
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Now, rewrite the expression: \[ \frac{0.0002}{4 \times 10^{-3}} = \frac{2 \times 10^{-4}}{4 \times 10^{-3}} \]
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This can be separated as follows: \[ \frac{2}{4} \times \frac{10^{-4}}{10^{-3}} \]
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Simplifying \( \frac{2}{4} \): \[ \frac{2}{4} = \frac{1}{2} = 0.5 \]
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Now simplify \( \frac{10^{-4}}{10^{-3}} \) using the property of exponents: \[ \frac{10^{-4}}{10^{-3}} = 10^{-4 - (-3)} = 10^{-4 + 3} = 10^{-1} \]
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Now combine the results: \[ 0.5 \times 10^{-1} = 5 \times 10^{-2} \]
So, the expression \( 0.0002 \div (4 \times 10^{-3}) \) simplifies to \( 5 \times 10^{-2} \).
The correct answer is: C. \( 5 \times 10^{-2} \).