Question

is the approximate relation celsius = 1/2 fahrenheit a better approximation at higher or lower temperatures?

Answer 1

Answer : The approximate relation Celsius = 1/2 Fahrenheit is a better approximation at higher temperatures

Explanation :

The formula for Celsius to Fahrenheit conversion is

$C = (F-32) \times \frac{5}{9}$

At lower temperature the value that needs to be subtracted (32) is large enough as a result the approximation "celsius = 1/2 fahrenheit " does not seem valid.

For example, 50 F is 10°C.

$(50 - 32) \times \frac{5}{9} = 10 C$

This is almost 1/5 of Fahrenheit temperature.

But at higher temperatures , the value becomes insignificant and also the ratio  5/9 tend to be equal to 0.5.

For example, 2000 F is 1093°C

$(2000 - 32) \times \frac{5}{9} = 1093 C$

This is almost half of Fahrenheit temperature.

Therefore , the approximate relation Celsius = 1/2 Fahrenheit is a better approximation at higher temperatures