Derive relationship between celsius and fahrenheit scale [closed]








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My book derives relationship between Celsius and Fahrenheit scale as



> 
> F-32/212-32 = C-0/100
> 
> 
> F-32/180 = C/100
> 
> 
> 


but I don't understand why F-32 is divided by 180? What does 180 and 100 indicate in both respectively?




Water boils at $100\ ^{\circ}\mathrm{C}$ and $212\ ^{\circ}\mathrm{F}$, while it freezes at $0\ ^{\circ}\mathrm{C}$ and $32\ ^{\circ}\mathrm{F}$. The numerators in formula provides the correct shift based on freezing point. The denominators provide the correct scaling between units by noting that a $180\ ^{\circ}$ increase on the Fahrenheit scale is equal to a $100\ ^{\circ}$ increase on the Celsius scale.


Note that your formula is missing some parentheses for correctness:


$$\frac{F-32}{212-32} = \frac{C-0}{100}$$ should be written as
$$(F-32)/(212-32) = C/100$$


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