Final answer:
To convert the speed of light to astronomical units per year, multiply the speed of light by the number of seconds in a year and then divide by the length of an astronomical unit.
Step-by-step explanation:
To convert the speed of light to astronomical units (ua) per year, we need to calculate the distance light travels in one year. The speed of light is approximately 300,000 km/s. Since there are 365 days in a year, we multiply the speed of light by the number of seconds in a day (24 hours x 60 minutes x 60 seconds) and then multiply by 365.
So, the speed of light in 1 year is approximately 9.46 x 10^12 km/year. To convert this to astronomical units, we divide by the length of an astronomical unit (1.50 x 10^8 km).
Therefore, the correct answer is a) 299,792,458 ua/year.