$383 \times 38 \times 3.8 = $x$

### Concept & Logic Decimal multiplication is identical to whole number multiplication, followed by placing the decimal point based on the total sum of decimal places in all factors. ### Step-by-Step Solution **Given:** $383 \times 38 \times 3.8$ First, ignore the decimal and multiply the numbers as integers: $383 \times 38 \times 38$ Calculate $38 \times 38$: $38^2 = 1444$ Multiply by $383$: $383 \times 1444 = 553052$ Now, count the total decimal places in the original expression. There is exactly $1$ decimal place (from $3.8$). Place the decimal point one digit from the right: $55305.2$ ### Exam Strategy & Shortcut Use the unit digit technique to save significant time. The unit digits of the original numbers (ignoring the decimal for a moment) are $3, 8, \text{ and } 8$. $3 \times 8 = 24$ (ends in $4$) $4 \times 8 = 32$ (ends in $2$) The final product must end in a $2$. Looking at the options, only option (a) ends in $.2$. This solves the problem in seconds without executing the full massive multiplication. ### Common Pitfall Unnecessarily calculating the entire multi-digit product. In competitive exams, questions with large multiplications almost always have a unit digit or digital root shortcut intended by the examiner. ### Final Answer Therefore, the correct answer is $55305.2$.