Celsius to Fahrenheit - simple math, but why not "symmetrical"?
As a pilot I need often the conversion from Celsius to Fahrenheit and backwards. I had to do during flying, without any tools (such as using a calculator).
So, some people "say" in Internet as a simplified method:
"take Celsius times 2 plus 30"
But this is very rough and not really correct. For 15C, times 2 equals 30 plus 30 gives me 60F". It should be 59F (as any pilot knows: 15C is 59F, the standard temperature reference for pilots).
But on higher temperatures, like soldering electronics, I need to convert 300C to F: the same trick is completely wrong: 300C times 2 equals 600 plus 30 would be 630F. But it must be for 300C a result as 572F (way too high with this simplification (works only around 15C).
So, the correct formula for converting Celsius to Fahrenheit is:
Fahrenheit = Celsius times 5 / 9 plus 32
When I see this and remember math correctly (that a divide is like doing N substractions), I can do this:
"Celsius times 2 - remember this result, divide it by 10 and substract this from the interim result. Add 32 at the end."
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Divide by 5 / 9 is like: divide by 5 / 10 ( a half) and add 1/10 back of the interim result (in order to get this times 5 / 9 done correctly).
So: 15C times 2 equals 30. Remember 30 and divide by 10 equals 3. Substract now from the interim result 30 this 3: equals 27. Add the offset 32 equals 59F.
Perfect! This works also for 300C: 300C * 2 = 600, 600 - 60 = 540, plus 32 = 572F, Also perfect.
But: why it does not work "symmetrical"? I mean: why "inverting" the steps done does not give me the correct result when doing backwards from F to C.
Example:
572F minus 32 = 540, plus 54 (the 1/10) = 594, divide by 2 = 297C. It is not 300C!
Why it is not "symmetrical"?
If I add a "rounding up trick" as a step, like: 572F minus 32 = 540, plus 540 rounded to 600 and plus 1 / 10 of it (= 60), 600 divide by 2 gives me 300C. it works in the same way with 59F: 59F minus 32 = 27, round it to 30 and plus 1 / 10 of it (= 3), is 60, divide by 2 results in 15C.
But why I have to add this "rounding up" here? Why from F to C the "inverted operation steps" do not end up with the correct result? Why is my procedure not "symmetrical"?