Question 7

Evaluate using scientific notation; with the decimal part rounded to three significant digits when necessary.
\[
\left(5.4 \times 10^{-6}\right)\left(1.8 \times 10^{-6}\right)\left(4.2 \times 10^{7}\right)
\]
$4.082 \times 10^{3}$
$4.08 \times 10^{-3}$
$4.082 \times 10^{4}$

Answer

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Answer

$\boxed{4.082 \times 10^{-4}}$

Steps

Step 1 ：Multiply the numbers: $5.4 \times 1.8 \times 4.2 = 40.824$

Step 2 ：Add the exponents: $-6 + -6 + 7 = -5$

Step 3 ：Convert to scientific notation: $40.824 \times 10^{-5} = 4.0824 \times 10^{-4}$

Step 4 ：Round to three significant digits: $4.0824 \times 10^{-4} = 4.082 \times 10^{-4}$

Step 5 ：$\boxed{4.082 \times 10^{-4}}$