To multiply the numbers \(4 \times 10^{-2}\) and \(1.3 \times 10^{-1}\), you can follow these steps:
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Multiply the coefficients: \[ 4 \times 1.3 = 5.2 \]
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Add the exponents of the powers of 10: \[ 10^{-2} \times 10^{-1} = 10^{-2 + (-1)} = 10^{-3} \]
Combining both results, you get: \[ 5.2 \times 10^{-3} \]
Thus, the final answer is: \[ 5.2 \times 10^{-3} \]