This is actually pretty important to being able to solve engineering problems in the real world. Invariably, every little sub industry has its own cursed unit system. And dimensional analysis is great for solving real problems on its own.
And if you get to a high enough physics level, they start setting hbar = c = 1 or G = c = 1, and you never have to worry about it again.
I'm the mean time, it's worthwhile to learn the trick to do this stuff fast-ish.
kWh has an intuitive reason. Watts are so small that you'd always calculate consumption in MJ and whatnot, and seconds are so short that you'd always be expressing time in ks. Using kWh will reduce the numbers to useful ranges and makes cancelling M and k unnecessary.
I used to do it this way in highschool, but could never remember if it was divide by or multiply by 3.6
Instead I now do it as you have shown, except it all goes in the same expression.
10 km/h * 1000 m/km * 1h/3600s = 2.778 m/s
No need for the extra steps. Slap it all in the same expression and put it in the calculator (being careful to check that the units cancel as intended)
M/s is faster (lower number) than km/h so... That should give you enough explanation to understand whether you need to divide or multiply 3.6 when converting.
That’s interesting. Obviously, you’d put a center dot to disambiguate millihertz from meter-hertz, but I can’t recall ever having learned a rule about that. So some combinations of units are inherently ambiguous?
I don't have time to get out a million little differently sized utensils because I need 2 cups of this, ¼ cup of that, ½ a teaspoon of the third thing etc. when I can put the bowl on a kitchen scale and use the tare function.