Are there really 9,460,000 km in a light year?

[Physicist50]

I was wondering if my measurements book that states there are 9,460,000 km in a lightyear is correct. I raise this question because I have recently done some calculations that resulted in my answer being 90,450,800,000,000 km in a LY. How I got this; a light year is how far a light beam travels in a year, and there are 31,536,000 seconds in a year, (1x60x60x24x365). The typical speed light travels at is 300,000,000 m/s. So the obvious calculation to do is 300,000,000 x 31,536,000 ÷ 1,000, which is 9,460,800,000,000. Have I done something wrong in my calculations, or am I right?

 

[Sourabh N]

You are right.

 

[Physicist50]

Thank you, and I thought books were the information source you can always rely on!

 

[Drakkith]

The speed of light is not actually 300,000 km per second, it is 299,792,458 m/s. (299,792 km/s) And your book is probably rounding anyways, which is perfectly fine with such a large number. It is not wrong.
Edit: Just noticed that your first number is missing like 6 zero's. Yeah, that's a BIT off...

 

[jbriggs444]

If we are to take the original posting as an accurate reflection of the book then the book is off by a factor of about one million. Possibly it was intending to report a distance in millions of km.

On the other hand, OP reports two results, one of which is wrong due to an apparent transcription error and the second of which is good to three significant figures.

9.46 x 10^6 quoted from book
9.045 x 10^13 first reported by OP
9.46 x 10^12 next reported by OP
9.467 x 10^12 per my calculations.

The length of the tropical year is somewhat greater than 365 days. I used 365.25 as a better approximation.

 

[Integral]

...
9.46 x 10^6 quoted from book
9.045 x 10^13 first reported by OP
9.46 x 10^12 next reported by OP
9.467 x 10^12 per my calculations.

...

Without units these numbers are meaningless.

 

[jbriggs444]

Without units these numbers are meaningless.

Good point. All figures were either intended or reported to be km/light-year.

 

[Drakkith]

Whoa, I just noticed the missing zero's in the OP's first post lol. Yeah, if that's what is quoted from the book then it's WAY off. Now I feel like a moron lol.