What percent is 1 minute and 12 seconds of an hour?

### Concept & Formula Before determining a percentage ratio, all quantities must be expressed in the exact same unit of measurement. The core concept here is converting mixed time units into a single common unit (seconds) before applying the percentage formula. $$ \text{Percentage} = \left( \frac{\text{Target Time in Seconds}}{\text{Base Time in Seconds}} \right) \times 100 $$ ### Step-by-Step Solution **Given:** * Target Time = $1$ minute and $12$ seconds * Base Time = $1$ hour **Calculation / Deduction:** * Convert the Target Time entirely into seconds. We know $1$ minute = $60$ seconds. $60 \text{ seconds} + 12 \text{ seconds} = 72 \text{ seconds}$ * Convert the Base Time ($1$ hour) entirely into seconds. We know $1$ hour = $60$ minutes, and $1$ minute = $60$ seconds. $60 \times 60 = 3600 \text{ seconds}$ * Set up the percentage fraction: $$ \left( \frac{72}{3600} \right) \times 100 $$ * Simplify the expression by cancelling the two trailing zeros in $3600$ with the $100$: $$ \frac{72}{36} $$ * Perform the final simple division: $72 \div 36 = 2$ * The resulting value is $2\%$. ### Exam Strategy & Shortcut You can also solve this efficiently using minutes as the base unit to keep the numbers smaller. Target Time: $12$ seconds is $\frac{12}{60}$ minutes, which is $0.2$ minutes. So, Target = $1.2$ minutes. Base Time: $1$ hour = $60$ minutes. Setup: $\frac{1.2}{60} \times 100$. Multiply $1.2 \times 100$ to get $120$. Then divide: $\frac{120}{60} = 2\%$. This method uses smaller baseline numbers and is faster for mental math. ### Common Pitfall The primary mistake is failing to standardize the units. A student might try to write the target time as $1.12$ (treating seconds directly as decimals of a minute) and dividing by $1$, leading to a wildly incorrect and confusing calculation. Always convert fully to the smallest shared unit. ### Final Answer Therefore, the correct answer is **2%**.