To multiply the scientific number \( 4.82 \times 10^1 \) by \( 256.7 \), we will first perform the multiplication on the numerical parts and then combine that with the power of ten.
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Start with the scientific number: \[ 4.82 \times 10^1 \]
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\( 10^1 \) is equal to 10, so we can write: \[ 4.82 \times 10 = 48.2 \]
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Now we will multiply \( 48.2 \) by \( 256.7 \): \[ 48.2 \times 256.7 \]
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Performing the multiplication: \[ 48.2 \times 256.7 = 12347.14 \]
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Now we can express this result in scientific notation. To convert \( 12347.14 \) to scientific notation, we move the decimal point four places to the left: \[ 1.234714 \times 10^4 \]
Thus, the final result of multiplying \( 4.82 \times 10^1 \) by \( 256.7 \) is: \[ 1.234714 \times 10^4 \]