Yes, it's difficult to make people think about it. At the same time, sometimes the units "don't matter" (like speed limits, 50 is 50 in the speedometer, just make sure you're not looking at the mph scale)
I want to slap somebody when I hear about "pounds" or "feet/sq ft", or even worse, Fahrenheit (since this is a non-linear transform)
At least everything in the supermarket is marked per pound and kilo
huh?
1. F(c1 + c2) = F(c1) + F(c2)
2. F(k*c1) = k*F(c1)
F(c) = 9/5 * c + 32
F(c1 + c2) = 9/5 * (c1 + c2) + 32
F(c1) + F(c2) = (9/5 * c1 + 32) + (9/5 * c2 + 32) = 9/5 * (c1 + c2) + 64
F(k*c1) = 9/5 * (k*c1) + 32
k*F(c1) = k * (9/5 * c1 + 32) = 9/5 * (k*c1) + k*32
Because it's harder to calculate mentally
One can approximate 2lb to 1kg roughly, 1mi ~ 1.6km, but for Fahrenheit this is harder
One solution is to establish a set point ( 70F = 21.1C, approximate to 20C ) then work in differences, since 1.8deltaF = 1deltaC so, 2dF ~ 1dC (or 10dF ~ 5dC)
Hence, 90F is approximately 30C (exact value, 32.2C)
I would think this would be called linear, but that mean something more specific?
For example, yards to meters is a linear transform. 3 yards converted to meters + 2 yards converted to meters = 5 yards converted to meters. This is not true of temperature. Adding 32F to 32F gives 64F, which is not the same as adding 0C to 0C.