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Physics constants help!?

I have a question about constants. If you have a constant, such as the Stefan-Bolzmann constant, when you use it in an actual equation, do you use just the number part? Like, do you just use the 5.67 x 10^-8 or do you use the units after it? The W/m^2/K^4? Do these units matter? I also have a book that lists it as 5.67 x 10^-8 J(s-m^2-K^4). Is this correct? I know that Joules/second is Watts, but it's not "per." That's only when you divide. Within the parentheses, it becomes multiplication, and that would be J x s instead of J/s, and I don't think a Joule times a second is a Watt. The book lists it as that, while another book I have (as well as the internet) lists it as 5.67 x 10^-8 W/m^2/K^4. Here is a summary of the two constants. Physics for Dummies: 5.67 X 10^-8 J(s-m^2-K^4) [The wrong one, I think] Physics demystified (and the inernet) 5.67 x 10^-8 W/m^2/K^4 And when you use any constant, do you use just the numbers or do you use the units (Watts, meters, etc)?

Public Comments

1. You should use the units with the constant. When you use SI units, it should all come out correctly. The "official" value is 5.670 400 x 10^-8 W m^-2 K^-4, plus or minus 40 in the last two digits. The units J(s-m^2-K^4) would be correct if you insert the missing "/" sign: J / (s-m^2-K^4).
2. always use the units, for in multiplication or division they will square or cancel
3. I routinely use the units in a physical constant to ensure the units work out for my answer. For instance, let's use the simple equation F = ma. The acceleration due to gravity is 9.8 m/s^2. So, when I have a mass, I know it must be in kg to make the right side units equal the left side units (Newtons, or kg-m/s^2). As far as the definitions you see in your books, I would guess that by putting the parentheses around s-m^2-K^4, it means to divide by that. Otherwise, if they meant to multiply, there would be no need for the parentheses.
4. The correct way of writing is W m^-2 K^-4 Since W = J s^-1. We can write the above as J s^-1m^-2 K^-4. If we write the above as W/m^2/K^4 it reads W per m^2 per K^4. This is ambiguous because it can be read in two ways; (W per m^2) per K^4 or W per (m^2 per K^4). In the second one, m^2 per K^4 is m^2 K^-4 and hence W per (m^2 per K^4) is W m^- 2 K^4 It is the reason that SI system recommends only the usage of ± symbols for powers and opposes the usage of “/” which always leads to confusion. Now use the correct one W m^-2 K^-4 and defy all other forms. However you can write as J s^-1m^-2 K^-4. Units are as important as magnitudes. Except the ratio of two same quantities, all others must be accompanied by appropriate units. .