beavith wrote:

[snip]

ceebee mentioned that the Hubble Constant is figured to be 74km/s/Mpc
where km is, of course, kilometers, s is seconds and Mpc is
megaparsecs.

my old HS physics teacher would always admonish us to "watch the
units." our old grade school math teachers would also tell us to
reduce our fractions.

here's the conundrum: if Mpc is roughly 3.25 million parsecs, and km

Light-years, not parsecs.

is another distance, if you reduce the Hubble constant to its basic
terms, won't you get a number with a unit of km^2/s?

Umm, no. Speed, distance-per-time, divided by distance is just
inverse time, here s^-1. Unless I've fouled up my arithmetic H = 74
km/s / Mpc = 2.4 * 10^-18 /s. This is a proportional rate, the
quantity that changes over time being dimensionless -- very like an
interest rate (percentages being dimensionless quantities in disguise).

if so, why do we keep the Hubble Constant in such a confusing batch of
units? it'd be like measuring an expanding balloon in X
in/sec/mile...

Because these units are appropriate to the observations on which the
constant is based: a typical galactic recession velocity can be
written in km/s without using a cumbersome exponential notation, and
likewise for most intergalactic distances when given in Mpc. If you
were working on an inflatable dome covering a large American city
(supposing there were such a thing) you might find measuring its
expansion in (in/sec)/mi to be very convenient! At least it might be
more intuitive for some than the 'cancelled-out' version, 0.0000158/s.

There are plenty of circumstances where 'unreduced' units are used
for practical applications; a few such are quite well established.
Take for example the kilowatt-hour: although megajoules would be a
more 'proper' measure for energy -- 1 kW·h = 3600 kW·s = 3.6 MJ -- it
seems that power companies find the former units more convenient.

does this mean that the surface of our universe is growing by this
area every second?

No, although I think one might say that all sufficiently large
distances grow proportionally by that amount, somewhat under one part
in ten billion per year UIFUMA. The surface area of a given region of
intergalactic space would then increase in a square proportion, and
its volume in a cubic.

--
Odysseus