-40 (number)

From Academic Kids

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.

See also

Fahrenheit - Celsius

sl:-40 (število)
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