To multiply two numbers in scientific notation, you can multiply the coefficients (the numbers in front) and then add the exponents of the powers of ten.
Given: \[ (2.3 \times 10^7) \times (5.4 \times 10^2) \]
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Multiply the coefficients: \[ 2.3 \times 5.4 = 12.42 \]
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Add the exponents: \[ 7 + 2 = 9 \]
So, combining these results gives: \[ 12.42 \times 10^9 \]
Since \(12.42\) is not between \(1\) and \(10\), we need to convert it to proper scientific notation. This can be done by moving the decimal point one place to the left, which increases the exponent by 1.
Thus: \[ 12.42 \times 10^9 = 1.242 \times 10^{10} \]
Therefore, the result in scientific notation is: \[ 1.242 \times 10^{10} \]