Calculating distance using redshift

[Goldilocks32]

Hi. I have pretty rudimentary math skills, and am hoping someone can explain this formula for me, found online a number of places including:

http://www.astrophysicsspectator.com/topics/overview/DistanceExtragalactic.html

for calculating distance (d) in megaparsecs using redshift (z), the speed of light (c), and Hubble's constant (H).

d = c z/H

It's the (units in) Hubble's constant that have me confused. In the example from the link, "we see that objects with a redshift of 0.1 are about 4.6 gigaparsecs [a]way", assuming an H of 65 km s-1 Mpc-1. So I assumed c here would be in km/s, but:

300000 * (0.1/65) = 461

Which is 0.46 gigaparsecs, not 4.6. What is it about the units/Hubble's constant here that I don't get?

Here's what I guessing: units ^ -1 mean 65 should be multiplied by 0.1, which is different than 65 ^ -1. This would make H 6.5, and the result would be correct. Is that right? If so, why is the notation km/s-1/Mpc-1? How would that be different from km/s/Mpc-1?

 

[zhermes]

I think your calculation (as it was) is correct. Your guess about the units is definitely not right---the units are separate from the number attached to them.
Maybe their result is just a typo...

 

[Goldilocks32]

Yeah, you're right. The next thing I tried this on was the Large Magellanic Cloud, which produced even more bizarre results, but I found a calculator for this online:

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/hubble.html#c3

And eventually got some data to match up (it seems the LMC's redshift is an anomaly, so my first test case was a typo and my second anomalous -_-).

 

[zhermes]

Haha, just some bad luck I guess!
Way to be thorough---good job