Question

To convert a temperature in degrees Celsius to degrees fahrenheit, multiply the celsius temperature by 9/5 and then add 32. Is a temperature in degrees Celsius proportional to it's equivalent temperature in degrees fahrenheit?

Answer 1

The relationship between degrees Celsius and Fahrenheit is not purely proportional due to the additional 32 degrees in the conversion formula. Proportionality requires a constant ratio, and the addition of 32 when converting Celsius to Fahrenheit disrupts this requirement.

Step-by-step explanation:

To determine whether a temperature in degrees Celsius is proportional to its equivalent temperature in degrees Fahrenheit, we need to examine the conversion formula. The formula to convert Celsius to Fahrenheit is T°F = (1.8 × T°C) + 32. Proportionality requires a constant ratio, which in this case would only be the multiplication factor. Because of the addition of 32, the relationship isn't purely proportional, as the conversion does not pass through the origin (0,0), which would signify direct proportionality.

The step-by-step example of the Celsius to Fahrenheit conversion is as follows:

1. Start with the Celsius temperature you wish to convert (for example, 25°C).
2. Multiply this value by 9/5 or 1.8 to convert to Fahrenheit degrees (25°C × 1.8 = 45°F).
3. Add 32 to the result (45°F + 32 = 77°F).
4. The final result is the temperature in Fahrenheit (77°F).

This procedure applies to all temperatures you wish to convert from Celsius to Fahrenheit. For example, 0°C is 32°F, and 100°C is 212°F, which shows an addition of 32 each time, disrupting the constant ratio required for pure proportionality.