The expression $\frac{(0.1667)(0.8333)(0.3333)}{(0.2222)(0.6667)(0.1250)}$ is approximately equal to

### Concept & Strategy Recognize standard recurring decimal fractions and convert them to their exact rational fractional forms ($p/q$) to simplify the entire product instantly. ### Step-by-Step Solution * Convert each decimal value to its exact fraction equivalent: * $0.1667 \approx \frac{1}{6}$ * $0.8333 \approx \frac{5}{6}$ * $0.3333 \approx \frac{1}{3}$ * $0.2222 \approx \frac{2}{9}$ * $0.6667 \approx \frac{2}{3}$ * $0.1250 = \frac{1}{8}$ * Rewrite the complete expression using these fractions: $$ \text{Numerator} = \frac{1}{6} \times \frac{5}{6} \times \frac{1}{3} = \frac{5}{108} $$ $$ \text{Denominator} = \frac{2}{9} \times \frac{2}{3} \times \frac{1}{8} = \frac{4}{216} = \frac{1}{54} $$ * Divide the numerator by the denominator: $$ \text{Value} = \frac{5}{108} \div \frac{1}{54} = \frac{5}{108} \times 54 $$ $$ = \frac{5}{2} = 2.50 $$ ### Exam Strategy & Shortcut Cancel matching items early in fractional format: $$ \frac{\frac{1}{6} \times \frac{5}{6} \times \frac{1}{3}}{\frac{2}{9} \times \frac{2}{3} \times \frac{1}{8}} $$ The $\frac{1}{3}$ terms cancel out. Notice $\frac{2}{9} \times \frac{1}{8} = \frac{1}{36}$, and $\frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$. These cancel completely, leaving just $\frac{5}{2 \times 2}$ forms or straightforward evaluation yielding $2.50$. ### Common Pitfall Attempting long decimal multiplication or imprecise rounding approximations, which leads to floating errors near $2.40$ or $2.43$. ### Final Answer **Therefore, the correct answer is 2.50.**