We simply double and add 30 to convert Celsius to Fahrenheit using approximation....

Question

To change a temperature from degrees Celsius to Fahrenheit you can multiply by 9, divide by 5 then add 32. An approximate method is to simply double and add 30. For what range of temperatures is the approximate method within one degree of the accurate method?

Answer 1

Let C be temperature in degree Celsius and F be that in Fahrenheit.
Then for the mentioned accuracy range
[9C/5+32] - [2C+30] = 1 or -1 {-1 and 1 being the tolerance on the accuracies}
It turns out that for these two equations to agree with one another with an accuracy mentioned above the Celsius temperature range has to be 5°C to 15°C {41°F to 59°F}.