What decimal of an hour is a second?

### Concept & Formula To express one unit of time as a decimal fraction of a larger unit, establish the ratio between them. $$\text{Decimal Fraction} = \frac{\text{Target Unit}}{\text{Total Base Units}}$$ ### Step-by-Step Solution * **Step 1: Convert the base unit (hour) to the target unit (seconds).** $1 \text{ hour} = 60 \text{ minutes}$ $1 \text{ minute} = 60 \text{ seconds}$ $$1 \text{ hour} = 60 \times 60 = 3600 \text{ seconds}$$ * **Step 2: Set up the fraction.** We want to find what fraction $1$ second is out of $1$ hour ($3600$ seconds). $$\text{Fraction} = \frac{1}{3600}$$ * **Step 3: Convert the fraction to a decimal.** To calculate $\frac{1}{3600}$, first find $\frac{1}{36}$. $$\frac{1}{36} = 0.02777...$$ Now divide by an additional $100$ (to account for the two zeros in $3600$). $$\frac{0.02777...}{100} = 0.0002777...$$ Rounding to the nearest significant digits provided in the options, we get $0.00027$. ### Exam Strategy & Shortcut Memorize that $\frac{1}{3} \approx 33.33\%$ and $\frac{1}{6} \approx 16.66\%$. Since $36 = 6 \times 6$, the value of $\frac{1}{36}$ must be slightly less than $\frac{1}{33}$ (which is $0.03$). Therefore, $\frac{1}{36}$ is roughly $0.027$. Adjusting for the two extra zeros in $3600$ shifts the decimal two places, resulting in $.00027$. This eliminates the need for long division. ### Common Pitfall A very common mistake is dividing by $60$ instead of $3600$, giving the decimal for a minute in an hour, rather than a second. Always ensure both the numerator and denominator are in the exact same unit before dividing. ### Final Answer **Therefore, the correct answer is .00027.**