Derive the formula for Celsius to Fahrenheit?

1 Answer

Answer:

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" #