Final answer:
To convert temperature from fractions to decimal numbers, specific conversion equations are used. The process involves plugging in the known values into the equations and solving for the desired unit. The relationship between temperature changes in Fahrenheit and Celsius is nine-fifths.
Step-by-step explanation:
Converting temperature from one scale to another involves using specific equations. In the instance provided, we need to convert temperatures from fractional representations to decimal numbers
To convert a temperature decrease of 40.0°F to Celsius, we use the equation (T°F - 32) × 5/9 = T°C, which gives us the temperature change in Celsius when starting with Fahrenheit. The reverse equation, T°F = T°C × 9/5 + 32, is used for converting from Celsius to Fahrenheit.
The relationship between Fahrenheit and Celsius scales is such that a change in Fahrenheit temperature is nine-fifths the change in Celsius degrees. To find temperature levels where Fahrenheit and Celsius scales intersect (i.e., have the same numerical value), we set T°F equal to T°C and solve for the temperature using the conversion equations.
Lastly, the Kelvin scale can be related by using Celsius to Kelvin conversion: T(K) = T(°C) + 273.15. To find where Fahrenheit and Kelvin scales have the same numerical value, we would convert a Fahrenheit temperature to Celsius and then to Kelvin using both equations subsequently.
It is always important to substitute the known quantities with their appropriate units into the relevant equations and to check the answers to ensure they are reasonable.