Question

Derive the formula for Celsius to Fahrenheit?

Answer 1

Compare the number of degrees from the freezing point of water to its boiling point on each scale to find a ratio and add in the differences between the freezing points.

Explanation:

The Fahrenheit freezing point of water is `32^@"F"` and its boiling point is `212^@"F"`.

`212^@"F" -32^@"F" = 180^@"F"` between the freezing point and boiling point of water.

The Celsius freezing point of water is `0^@"C"` and its boiling point is `100^@"C"`.

`100^@"C" -0^@"C" = 100^@"C"` between water's freezing and boiling points.

This results in a ratio for C to F of `100/180` or `5/9`, and
this results in a ratio for F to C of `180/100` or `9/5`.

Then `32^@"F"` equal `0^@"C"`, so

The formula for `""^@"C"` to `""^@"F"` is

`( ""^@"C" xx 9/5 )+ 32 = ""^@"F"`