The value of $$ \frac{489.1375 \times 0.0483 \times 1.956}{0.0873 \times 92.581 \times 99.749} $$ is closest to

### Strategy & Logic Just like the previous problem, the phrase "closest to" combined with options that differ strictly by a decimal place magnitude ($0.006, 0.06, 0.6, 6$) signals that you should use **Aggressive Approximation**. We need to find the order of magnitude, not the exact digit. ### Step-by-Step Solution **Given:** $$ \frac{489.1375 \times 0.0483 \times 1.956}{0.0873 \times 92.581 \times 99.749} $$ **Deduction (Approximation):** * Round each term to the nearest easy-to-use whole number or clean decimal: * $489.1375 \approx 500$ (or $490$) * $0.0483 \approx 0.05$ * $1.956 \approx 2$ * $0.0873 \approx 0.09$ (or $0.1$) * $92.581 \approx 90$ (or $100$) * $99.749 \approx 100$ * Let's use these rounded values to rewrite the expression: $$ \frac{500 \times 0.05 \times 2}{0.09 \times 90 \times 100} $$ * Calculate the approximate numerator: $500 \times 0.05 = 25$ $25 \times 2 = 50$ * Calculate the approximate denominator: $0.09 \times 90 = 8.1$ $8.1 \times 100 = 810$ * Evaluate the approximate ratio: $$ \frac{50}{810} = \frac{5}{81} $$ * Since $5/80$ would be exactly $1/16$, and we know $1/16 = 0.0625$, the value $5/81$ is very close to $0.06$. * Checking the options, $0.06$ perfectly matches our approximated order of magnitude. ### Exam Strategy & Shortcut **Magnitude Tracking:** You can simplify the order of magnitude visually. Numerator is roughly: $500 \times (5 \times 10^{-2}) \times 2 = 50$. Denominator is roughly: $(1 \times 10^{-1}) \times 100 \times 100 = 1000$. $50 / 1000 = 0.05$. The closest option to $0.05$ is $0.06$. This confirms that the magnitude is in the hundredths place, instantly eliminating $0.006, 0.6,$ and $6$. ### Common Pitfall Rounding down too many terms in the denominator (e.g., making it $0.08 \times 90 \times 90$) while rounding up the numerator. This can skew your final fraction slightly. Always try to round one term up and another down to balance the error, though in magnitude-based questions, minor skewing rarely changes the final answer. ### Final Answer **Therefore, the correct answer is 0.06.**