Question

Why temperature is the same whether it is expressed in the celcius or the fahrenheit scale

Answer 1

The Celsius and Fahrenheit are two important temperature scales. The Fahrenheit scale is used primarily in the United States, while Celsius is used throughout the world. The two scales have different zero points and the Celsius degree is bigger than the Fahrenheit one. There is one point on the Fahrenheit and Celsius scales where the temperatures in degrees are equal. This is -40 °C and -40 °F. If you can't remember the number, there is a simple algebraic method to find the answer.

Setting Fahrenheit and Celsius Equal

Rather than converting one temperature to another (not helpful because it assumes you already know the answer), you set degrees Celsius and degrees Fahrenheit equal to each other using the conversion formula between the two temperature scales:

°F = (°C * 9/5) + 32
°C = (°F - 32) * 5/9

It does not matter which equation you use. Simple use "x" instead of degrees Celsius and Fahrenheit. You can solve this problem by solving for x:

°C = 5/9 * (°F - 32)
x = 5/9 * (x - 32)
x = (5/9)x - 17.778
1x - (5/9)x = -17.778
0.444x = -17.778
x = -40 degrees Celsius or Fahrenheit

Working using the other equation you get the same answer:

°F = (°C * 9/5) + 32
°x - (°x * 9/5) = 32
-4/5 * °x = 32
°x = -32 * 5/4
x = -40°