Question

problem set #1 begin date: 8/25/2025 12:01:00 am due date: 9/4/2025 11:59:00 pm end date: 9/7/2025 11:59:00 pm problem 7 in the units used in the u.s., the speed of light is roughly 670 million mi/hr. using the information in the problem statement, find approximately how many miles there are in a light-year.

Explanation:

Step1: Determine hours in a year

A year has 365 days, and a day has 24 hours. So total hours in a year: $365\times24 = 8760$ hours.

Step2: Calculate miles in a light - year

Speed of light is $670\times10^{6}$ mi/hr. Distance = Speed×Time. So distance (miles in a light - year) is $670\times10^{6}\times8760$.
First, $670\times8760 = 670\times(8000 + 700+60)=670\times8000+670\times700 + 670\times60=5360000+469000+40200 = 5869200$.
Then multiply by $10^{6}$: $5869200\times10^{6}=5.8692\times10^{12}$ miles (approx).

Answer:

Approximately $5.87\times10^{12}$ miles (or more precisely $5.8692\times10^{12}$ miles) are in a light - year.