Question

Find the percent change from the first value to the second.

a) The change is a decrease by 40%
b) The change is a decrease by 60%
c) The change is an increase by 40%
d) The change is an increase by 60%

Answer 1

The temperature decreases by 4.44 degrees Celsius when there is a 40.0°F decrease in temperature, and any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees.

Step-by-step explanation:

Fahrenheit to Celsius Conversion

To find the percent change in temperature from Fahrenheit to Celsius, we can use the formula for converting Fahrenheit (F) to Celsius (C): C = (F - 32) × 5/9. A decrease of 40.0°F would convert to Celsius as follows: C = (40.0 - 32) × 5/9 = 8.0 × 5/9 = 4.44°C. Therefore, the temperature decreases by 4.44 degrees Celsius when there is a 40.0°F decrease in temperature.

To show that any change in temperature in Fahrenheit degrees is nine-fifths the change in Celsius degrees, let us consider a change in temperature of ΔF in Fahrenheit and its equivalent ΔC in Celsius. Using the conversion formula, we can say that for every change of ΔF: ΔC = (ΔF) × 5/9. Therefore, the change in Fahrenheit is ΔF = ΔC × 9/5, which shows that the change in Fahrenheit degrees is indeed nine-fifths the change in Celsius degrees.