-40 (number)
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| Cardinal | -40 |
| Binary | -101000 or 11011000 in two's complement in a signed byte |
| Hexadecimal | -28, or D8 in two's complement in a signed byte |
Minus forty is:
- the temperature (in degrees) at which Celsius and Fahrenheit scales read the same; often referred to as 40 below.
This can be shown easily. To convert from Fahrenheit to Celsius, one subtracts 32, then multiples by 5/9. This is expressed mathematically as C = (5/9)(F − 32), where F = Fahrenheit and C = Celsius. Alternatively F = C(9/5) + 32 .
Therefore, to find this special temperature, choose a formula and set the variables equal, denoting a temperature that is the same in both scales:
F = F(9/5) + 32
(−4/5)F = 32
F = −40
or
C = (5/9)(C − 32)
(9/5)C = C − 32
(4/5)C = −32
C = −40
These are mathematically equivalent demonstrations.
Also, the Fahrenheit and Celsius temperature conversion formulae can be represented in the particularly nice forms (using -40)
- <math> F = \frac{9(C - (-40))}{5} + (-40)\,<math>
and
- <math> C = \frac{5(F - (-40))}{9} + (-40)\,<math>
which may be easier for mental calculation.