Does r depende on the units used to measure variables (e.g. dollars or cents, inches or feet)? Why or why not?

Answer 1

what is r?

The value of a variable in an equation will depend on the units that you are using for your measurements.

This may be even true for a constant. For example, the gravity at Earth's surface is 9.8 m/s^2. If you use F = ma to figure out the force that attracts a 100 kg mass towards the centre of Earth, you find:

F = 100 kg * 9.8 m/s^2 = 980 kg m / s^2 = 980 Newtons.

Of course, if you use an acceleration of 32.2 ft/s^2 (same as 9.8 m/s^2), and you want to know the mass of an object that get attracted by a force of 220 pounds, then you use:

F = ma
therefore
m = F/a = 220 lbs / 32.2 ft/s^2 = 6.83 lbs s^2 / ft = 6.83 slugs (that is the name of the unit of mass in that system -- I am not making it up). This is the same mass as 100 kg.

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So, I'd say that a value does depend on the units used.

Some constants are 'unit-free'. For example, the Cosine of 60 degrees = 0.5 (without any units); it is a pure value.

Answer 2

It really depends on who will be using the plan. If most of the people who use the plan are more accustomed to metric, use metric. Typically, that is outside of the US. If you use imperial, use feet and inches like this: 10'-3 1/2" means ten feet three and one half inches. 3'-0" means three feet Under one foot there are two conventions that are acceptable 10" or 0'-10" I just use 10", but either is OK, just be consistent. Doors and windows are measured in feet and inches, but are written, for example, like this: 2-8 means two feet eight inch 3-0 means three feet. Just like above, but without the feet and inch symbols. Don't ask me why, it is just conventionally accepted method. Windows you should indicate whether double hung or single hung by DH or SH respectively, after the window size. Doors you can tell by the symbol between a hinged door, bi-hinge, bi-fold, sliding, pocket, so if standard height of 6'-8", no other notation is really needed. There is one exception to measurements. Most of the kitchen designs done by kitchen designers I've seen use strictly inches. A cabinet run of 12' is noted as 144". A 3 feet cabinet is shown as 36". Perhaps it is regional convention.