How do you convert -40°C to °F?

Step by step breakdown of the conversion from Celsius to Fahrenheit :

Formula for Conversion:

The formula to convert Celsius (°C) to Fahrenheit (°F) is:

                                           °F=(9÷5×°C)+32

Where:

• °C is the temperature in Celsius.
• °F is the temperature in Fahrenheit.

Step-by-Step Breakdown:

1. Start with the given Celsius temperature:
   In this case, the temperature is -40°C.
2. Multiply by the fraction 9​÷5:
   The first part of the formula is multiplying the Celsius temperature by 9559​, or 1.8. This is done to scale the Celsius value into the larger Fahrenheit scale.

                             9​÷5×(−40)=−72

So, after this multiplication, we get –72.

3. Add 32 to the result:
After multiplying, you add 32 to the result. This accounts for the difference between the freezing points of water in both scales. Water freezes at 0°C, but at 32°F, so you add 32 to the Celsius result after scaling it to Fahrenheit.

                                                −72+32=−40

4. Final result:
After performing the calculation, we end up with –40°F.

The Remarkable Coincidence:

• –40°C and -40°F are exactly the same temperature. This is the only point where the Celsius and Fahrenheit scales meet. So, –40°C = -40°F. It’s a unique and interesting property of the temperature conversion.

Why the Formula Works:

The formula arises from the way the Celsius and Fahrenheit scales are structured:

• The Celsius scale is based on 0°C as the freezing point of water and 100°C as the boiling point (at sea level).
• The Fahrenheit scale uses 32°F for the freezing point of water and 212°F for the boiling point of water.

Because the Fahrenheit scale has smaller increments (1°F is 1/180 of the range between freezing and boiling points of water, while 1°C is 1/100 of that range), the scaling factor between the two systems is 9÷5​ (or 1.8). The +32 accounts for the difference in the zero points of the two scales.