Solution:
Here, temperature at Fahrenheit scale (F) = -40 ºF,
the temperature at Celsius scale (C) =?
From the temperature transformation formula we have,
\(\frac{C-0}{100}=\frac{F-32}{180}\)
Or, \(\frac{C-0}{100}=\frac{-40-32}{180}\)
Or, \(C=\frac{-72}{180}\times100\)
∴ C = -40ºC
Hence -40 ºC = -40 ºF
There is no special reason for this same value in different scales. It is a mere coincidence. Based on the definitions of the Fahrenheit scale and the Celsius scale -40ºF = -40ºC.