1 AU = 0.0000158 light-years
I don't think they are "important"; but they are convenient units of length - AU for distances within the Solar System (or other comparable distances); light-years (and parsecs) for larger distances.
The distance from the Sun to Sedna is approximately 86 astronomical units (AU). Since light travels at a speed of about 186,282 miles per second, it would take roughly 13.7 hours for light to travel from the Sun to Sedna. This is equivalent to around 822 minutes.
A light year is a measure of distance, not time. It is the distance light travels in a year.
the Crab-nebula is 6,500 light-years from Earth.
That would be "Beta Centauri". Wikipedia lists its distance as 350 ± 20 light-years. Wolfram Alpha lists a the distance as 397.4 light-years.
600 light-years is 37,944,646.2 AU
16 light years is 1,011,834.75 AU (Astronomical Units).
2.25 AU
They really are not comparable. Light travels 186,000 miles per second, and one AU is about 8.3 light-MINUTES. You can probably do the math, from minutes to hours to days to years as well as I can. Or, you could google "1000 light years in AU" and get the answer
1 light year is approximately 63,241 AU. Therefore, 4.7 light years is about 297,116 AU.
5.5 light years equates to 347,818.194 AU (Astronomical Units).
35.2 AU = roughly 0.000557 light-year (rounded)
The average distance between Mercury and Venus is approximately 0.5 astronomical units (AU), where 1 AU is approximately 93 million miles. One light year is about 63,241 AU, so the distance between Mercury and Venus is about 0.0000079 light years.
Saturn is approximately 9.5 AU from the sun, which is about 0.00015 light years.
The Milky Way is estimated to be about 2,000 light years thick, but about 100,000 light years long/far... Which i guess you can tell, thats a lot.
Jupiter is not even close to a light year from the sun. Jupiter is about 5.2 AU from the sun on average, which works out to about 43 light minutes.
Voyager 1 was able to perform measurements and establish the distance as 121 AU (18 billion km). This would make the distance about 0.0019 light years.