What percent of a day is $3$ hours?

### Concept & Formula To find what percentage a specific number of hours represents out of an entire day, you must standardise the units by converting the day into hours. $$ \text{Percentage} = \left( \frac{\text{Given Hours}}{\text{Total Hours in a Day}} \right) \times 100 $$ ### Step-by-Step Solution * **Given:** * Part = $3$ hours * Whole = $1$ day * **Deduction:** * Convert $1$ day into hours: $1 \text{ day} = 24 \text{ hours}$. * **Calculation:** * Substitute the values into the formula: * $\text{Percentage} = \left( \frac{3}{24} \right) \times 100$ * Simplify the fraction $\frac{3}{24}$ to $\frac{1}{8}$: * $\text{Percentage} = \frac{1}{8} \times 100 = \frac{100}{8}$ * Divide $100$ by $8$: * $\frac{100}{8} = 12.5\%$ * Convert $12.5\%$ into a mixed fraction: $12\frac{1}{2}\%$. ### Exam Strategy & Shortcut Memorize standard fraction-to-percentage conversions. Once you reduce $\frac{3}{24}$ to $\frac{1}{8}$, you should instantly know that $\frac{1}{8}$ always equals $12.5\%$ or $12\frac{1}{2}\%$. This eliminates the need for any actual calculation. ### Common Pitfall A careless mistake is using $12$ hours as the base for a "day" (thinking only of daytime) instead of the full $24$-hour cycle. Using $12$ would incorrectly result in $\frac{3}{12} = 25\%$. ### Final Answer **Therefore, the correct answer is $12\\frac{1}{2}\\%$.**