$0.04 \times 0.0162$ is equal to

Concept & Formula To solve this quickly and avoid counting zeros, convert the decimals into scientific notation before multiplying. Use the standard exponent multiplication rule: $$x^a \times x^b = x^{a+b}$$ Step-by-Step Solution * Convert the first decimal to scientific notation: $0.04 = 4 \times 10^{-2}$. * Convert the second decimal: $0.0162 = 162 \times 10^{-4}$. * Multiply the integer parts: $4 \times 162 = 648$. * Multiply the base-10 exponential parts: $10^{-2} \times 10^{-4} = 10^{-6}$. * Combine them: $648 \times 10^{-6}$. * Adjust to standard scientific notation (one digit before the decimal): $648 = 6.48 \times 10^2$. * Final calculation: $6.48 \times 10^2 \times 10^{-6} = 6.48 \times 10^{-4}$. Exam Strategy & Shortcut Count the decimal places. $0.04$ has 2, and $0.0162$ has 4. The product will have $2 + 4 = 6$ decimal places. So the number is $0.000648$. To write this as $6.48 \times 10^n$, you move the decimal point 4 places to the right, which means $n = -4$. Common Pitfall A very common mistake is simply adding the decimal places to get $10^{-6}$ and selecting option (d), completely forgetting that $648 \times 10^{-6}$ is NOT the same as $6.48 \times 10^{-6}$. Standard form requires moving the decimal point two more places. Final Answer **Therefore, the correct answer is $6.48 \times 10^{-4}$.**