$\frac{5.3472 \times 324.23}{3.489 \times 5.42}$ is the same as

### Concept & Logic For a complex fraction to maintain its value, the net decimal multiplier (total numerator decimal places minus total denominator decimal places) must remain identical across the original and equivalent expressions. ### Step-by-Step Solution * Analyze the decimal places in the original expression: Numerator: $5.3472$ ($4$ places) and $324.23$ ($2$ places) $\rightarrow$ Total $6$ places ($10^{-6}$). Denominator: $3.489$ ($3$ places) and $5.42$ ($2$ places) $\rightarrow$ Total $5$ places ($10^{-5}$). * Calculate the net shift of the original expression: Net multiplier = $\frac{10^{-6}}{10^{-5}} = 10^{-1}$. This means the raw integer fraction must be multiplied by $10^{-1}$. * Test the options to find the one with a net multiplier of $10^{-1}$: Option (a): Numerator ($0 + 4 = 4$), Denominator ($3 + 1 = 4$). Net = $10^0 = 1$. (Incorrect) Option (b): Numerator ($0 + 0 = 0$), Denominator ($0 + 0 = 0$). Net = $10^0 = 1$. (Incorrect) Option (c): Numerator ($2 + 2 = 4$), Denominator ($2 + 2 = 4$). Net = $10^0 = 1$. (Incorrect) Option (d): Numerator ($0 + 1 = 1$), Denominator ($0 + 0 = 0$). Net = $\frac{10^{-1}}{10^0} = 10^{-1}$. (Correct) ### Exam Strategy & Shortcut Sum the decimal places on top ($4+2=6$) and on bottom ($3+2=5$). The top has $1$ more decimal place than the bottom. Look at the options and find the one where the top has exactly $1$ more decimal place than the bottom. Only Option (d) has $1$ decimal place on top and $0$ on the bottom. ### Common Pitfall Assuming that clearing all decimals (as in Option b) creates an equivalent fraction. Clearing all decimals only works if the original numerator and denominator had the exact same number of total decimal places. ### Final Answer **Therefore, the correct answer is $\frac{53472 \times 3242.3}{3489 \times 542}$.**