$(.00625 \text{ of } \frac{23}{5})$ when expressed as a vulgar fraction, equals

Concept & Strategy The term "vulgar fraction" simply means a common fraction (a numerator over a denominator). The smartest strategy is to convert the given decimal into a fraction first, simplify it completely, and then perform the multiplication. Step-by-Step Solution * First, convert the decimal $0.00625$ into a fraction. Since there are 5 digits after the decimal, write it over $100000$: $$\frac{625}{100000}$$ * Simplify this fraction. Both numbers are divisible by 25: $$\frac{25}{4000}$$ * Simplify further. Both are divisible by 25 again: $$\frac{1}{160}$$ * Now substitute this back into the original expression. "Of" signifies multiplication: $$\frac{1}{160} \times \frac{23}{5}$$ * Multiply the numerators and denominators straight across: $$\frac{1 \times 23}{160 \times 5} = \frac{23}{800}$$ Exam Strategy & Shortcut Memorizing standard decimal-to-fraction conversions saves immense time. Knowing that $0.125 = \frac{1}{8}$ allows you to quickly deduce that $0.0625 = \frac{1}{16}$, and therefore shifting the decimal one more place means $0.00625 = \frac{1}{160}$. From there, it's a simple mental calculation: $160 \times 5 = 800$, leading straight to $\frac{23}{800}$. Common Pitfall Students often try to divide 23 by 5 first (getting 4.6) and then multiply $0.00625 \times 4.6$. While mathematically correct, it results in a complex decimal ($0.02875$) that is frustrating and time-consuming to convert back into a fraction. Always stay in fraction form. Final Answer **Therefore, the correct answer is $\frac{23}{800}$.**