$3 \times 0.3 \times 0.03 \times 0.003 \times 30 = $x$

### Concept & Strategy Group the base integer digits and the powers of $10$ separately. This prevents losing track of decimal places during chained multiplication involving both decimals and tens. ### Step-by-Step Solution **Given:** $3 \times 0.3 \times 0.03 \times 0.003 \times 30$ First, multiply all the non-zero integer components (there are five $3$s): $3 \times 3 \times 3 \times 3 \times 3 = 3^5 = 243$ Next, evaluate the decimal shifts and trailing zeros using powers of $10$: $0.3 = 10^{-1}$ $0.03 = 10^{-2}$ $0.003 = 10^{-3}$ $30 = 10^1$ Sum the exponents to find the net decimal shift: $-1 - 2 - 3 + 1 = -5$ Combine the integer product with the net power of $10$: $243 \times 10^{-5}$ Shift the decimal $5$ places to the left from $243$: $0.00243$ ### Exam Strategy & Shortcut Quickly sum the total decimal places: $1 + 2 + 3 = 6$ places. Notice the number $30$ has one trailing zero, which effectively cancels out one decimal place ($6 - 1 = 5$ net decimal places). Since $3^5 = 243$, we simply need $5$ decimal places for the integer $243$, directly yielding $0.00243$. ### Common Pitfall Forgetting to account for the trailing zero in "$30$" which actively reduces the total number of decimal places in the final answer by one. Students often leave it at $6$ shifts, resulting in the incorrect option (b). ### Final Answer Therefore, the correct answer is $0.00243$.