A star is $8.1 \times 10^{13}$ km away from the earth. Suppose light travels at the speed of $3.0 \times 10^5$ km per second. How long will it take the light from the star to reach the earth?

### Concept & Time-Distance Formula Time is calculated by dividing distance by speed. Pay attention to the units and convert seconds to hours if necessary. $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$ ### Step-by-Step Solution * Given Distance = $8.1 \times 10^{13}$ km. * Given Speed = $3.0 \times 10^5$ km/s. * Calculate time in seconds: $\text{Time} = \frac{8.1 \times 10^{13}}{3.0 \times 10^5} = 2.7 \times 10^8$ seconds. * Convert seconds to hours (since $2.7 \times 10^8$ is not an option): Divide by 3600 (60 minutes $\times$ 60 seconds). * Time in hours = $\frac{2.7 \times 10^8}{3600} = \frac{2700 \times 10^5}{36 \times 10^2} = 75 \times 10^3 = 7.5 \times 10^4$ hours. ### Exam Strategy & Shortcut Work with powers of 10 separately. $8.1 / 3 = 2.7$ and $10^{13} / 10^5 = 10^8$. You immediately get $2.7 \times 10^8$ seconds. Recognizing $3600$ seconds in an hour, $270/36 = 7.5$, giving you the mantissa 7.5 for the hour conversion. ### Common Pitfall Forgetting to convert the calculated time from seconds to hours, or miscalculating the exponents when dividing terms with powers of 10. ### Final Answer Therefore, the correct answer is **$7.5 \times 10^4$ hours**.