$0.1 \times 0.01 \times 0.001 = $x$

### Concept & Logic When multiplying pure decimal fractions of $1$, the result is simply a $1$ with the decimal point shifted left by the total sum of decimal places across all factors. ### Step-by-Step Solution **Given:** $0.1 \times 0.01 \times 0.001$ Count the decimal places for each individual term: $0.1 \rightarrow 1$ place $0.01 \rightarrow 2$ places $0.001 \rightarrow 3$ places Total decimal places = $1 + 2 + 3 = 6$ places. The non-zero integer multiplication is $1 \times 1 \times 1 = 1$. Place the decimal $6$ positions to the left of $1$: $0.000001$ ### Exam Strategy & Shortcut Convert to negative powers of $10$ for absolute accuracy without needing to count physical physical on the screen or paper. $10^{-1} \times 10^{-2} \times 10^{-3} = 10^{-6}$. $10^{-6}$ indicates the decimal is $6$ places to the left, which universally translates to $5$ visual zeros after the decimal point before the $1$. ### Common Pitfall Manually counting zeros instead of total decimal places. A very common mistake is thinking $1 + 2 + 3 = 6$ zeros, which would incorrectly lead you to select option (d) instead of the correct option (c). ### Final Answer Therefore, the correct answer is $0.000001$.