I think about the difference between the two using differences instead of absolutes. That looks like this:
It's kind of hard to do this calc:
F = [ (9/5) * C ] + 32
Or this one:
C = (5/9) * (F - 32)
I refer to those as absolute equations. You have to take into account the pesky offset everytime you want to convert. What if we drop it? This makes:
F = (9/5) * C = 1.8 * C
C = (5/9) * F ~= 0.6 * F
I refer to those as relative or difference equations because if you subtract a temperature from the other, you get the same thing:
F1 = [ (9/5) * C1 ] + 32
F2 = [ (9/5) * C2 ] + 32
F2 - F1 = [ (9/5) * C2 ] + 32 - { [ (9/5) * C1 ] + 32 }
= [ (9/5) * C2 ] - [ (9/5) * C1 ] + 32 - 32
= [ (9/5) * C2 ] - [ (9/5) * C1 ]
= (9/5) [ C2 - C1 ]
F2 - F1 = (9/5) (C2 - C1)
βF = (9/5) βC
So, why is this useful?
Say you have a temperature in Celsius and want to go to Fahrenheit. Simply multiply that number in your head by 1.8 (or think of this as multiplying by 180Β° as in trig) and finally add to 32. So, 1 Β°C is (1 * 1.8) + 32 Β°F or about 34 Β°F.
Going the other way is a little bit weirder. I make approximations when going the other way by thinking of 180Β° and how that can be divided. So, 180Β°, 90Β°, 45Β°, etc. corresponds to 1.8 Β°F (1 Β°C), 0.9 (0.5 Β°C), 0.45 Β°F (0.25 Β°C), etc. I also approximate by choosing the nearest multiple of 5 or 10 Β°C (9 or 18 Β°F). So, 44 Β°F is between 41 Β°F (5 Β°C) and 50 Β°F (10 Β°C), closer to 41. It's off by 3, which is about 3.6, which is 2 in Celsius world. This means 44 Β°F is about 7 Β°C.
Hope you get the gist! Celsius really is better. I remember this in a pinch:
10 Β°C = 50 Β°F
20 Β°C = 68 Β°F
30 Β°C = 86 Β°F
40 Β°C = 104 Β°F
50 Β°C = 122 Β°F
Etc.
The freezing temps are a little hard since you cross zero into negatives, but the extrapolation can help