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Homework Statement
Converting Hubble's constant in SI units of s1 into kms1 Mpc1 (kilometers per second per megaparsec)
Number given is 2.31 x 10^18 s1.
Homework Equations
H = v/d (where H is Hubble's constant, v = velocity and d = distance)
The Attempt at a Solution
I can see how you get the answer but it took me a while to see the reasoning for what to divide/multiply by. I reasoned that if you use H = v/d then 2.31 x 10^18 s1 can be rewritten as 2.31 x 10^18 ms1 m1 (meters per second per metre). I then treated the numerator and denominator separately. So to get from m/s to km per second you divide by 1000. Then to get from per metre to per megaparsec you multiply by the number of metres in a megaparsec. So overall you get 2.31 x 10^18 x 3.09 x 10^22 / 1000 which gives 71.4 kms1 Mpc1. Using the same logic I don't understand something on the additional notes in the mark scheme for this question. I have uploaded the question and markscheme. They have shown an example of if you forget to convert hubble's constant into s1 otherwise it will be in years1. They then work this answer through the same way and give less marks for it however they say that the units are still kms1 Mpc1 at the end but that seems wrong to me. If you take hubble's constant in years1 instead of seconds1 and then multiply by the same number and divide by the same number surely its impossible to end up with the same final units? or am I missing something?
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