Final answer:
A decrease of 40.0 Fahrenheit degrees corresponds to a decrease of approximately 22.2 Celsius degrees. This demonstrates that the Fahrenheit temperature change is nine-fifths the change in Celsius degrees, reflecting the difference in the scales used to measure temperature changes.
Step-by-step explanation:
Temperature Conversion from Fahrenheit to Celsius
When a cold front causes the temperature to drop by 40.0 Fahrenheit degrees, here is how you can calculate the decrease in Celsius degrees:
First, remember the formula for converting Fahrenheit to Celsius: C = (F - 32) × (5/9), where F is the temperature in Fahrenheit degrees and C is the temperature in Celsius degrees. However, when we’re talking about a change in temperature instead of an absolute temperature, the initial subtraction of 32 degrees is not necessary. Only the ratio of 5/9 is used because we are concerned with the change in degrees, not the actual temperature value.
So, in the case of a 40.0°F decrease, the calculation would be 40.0 × (5/9), which equals approximately 22.2 Celsius degrees.
To show that any change in Fahrenheit is nine-fifths the change in Celsius, you can use the reverse process. To convert from Celsius to Fahrenheit, the factor is (9/5). Therefore, a temperature change in Celsius multiplied by (9/5) will give you the temperature change in Fahrenheit. This illustrates that the Fahrenheit scale is nine-fifths of the Celsius scale when it comes to measuring temperature changes since 9/5 = 1.8, which is the ratio of the Fahrenheit degree span (180 degrees between the freezing and boiling points of water) to the Celsius degree span (100 degrees between those same two points).