Problem is: 58,000.000 KM being converted to light-years
I did 58,000,000 x 365 x 24 x 60 x 60 and came up with 0.0000006131 and converted that to 6 x 10 to the negative 6. My teacher says it should have been 6 x 10 to the negative 5? Could you explain where I went wrong? Thank you so much for any help you can give me.
Your answer is actually correct. It should be raised to -6, not -5. For the solution:
1 Light Year = 9.46 x 10^12 km
Thus,
58,000,000 km * (1 light year / 9.46 x 10^12 km)
= 6.131 x 10^-6 light year
Thank you Jai - I wish I had the nerve to tell her she was wrong, I tried that once and oh boy, let's just say things did not work out after that. I'll just know I was right and accept the 2 points off. Thank You again Kyle
To convert kilometers (KM) to light-years, we need to divide the distance in kilometers by the speed of light.
The speed of light is approximately 299,792 kilometers per second. To convert kilometers to light-years, we need to divide the distance in kilometers by the product of the speed of light and the number of seconds in a year.
Let's break it down step by step:
1. Start with the given distance in kilometers: 58,000,000 KM.
2. Convert the speed of light from kilometers per second to kilometers per year.
- There are 60 seconds in a minute, 60 minutes in an hour, and 24 hours in a day.
- There are 365 days in a year.
- Therefore, there are 60 x 60 x 24 x 365 = 31,536,000 seconds in a year.
- Divide the speed of light by the number of seconds in a year:
Speed of light in KM/year = 299,792 KM/sec / 31,536,000 sec/year ≈ 9.461 × 10^12 KM/year.
3. Divide the distance in kilometers by the speed of light in kilometers per year:
58,000,000 KM / 9.461 × 10^12 KM/year ≈ 6.129 × 10^(-6) light-years.
Based on your calculation, it seems you followed the correct steps, but there might have been a rounding error. Your result, 0.0000006131, rounded to the nearest sixth decimal place, should indeed be approximately 6.129 × 10^(-6) or 6.13 × 10^(-6) light-years, not 6 × 10^(-5) light-years. Double-check your calculations and make sure you're dividing by the correct value for the speed of light in KM/year.