Suppose a cold front blows into your locale and drops the temperature by 42.5 degrees fahrenheit. How many degrees Celcius is this temperature decrease? Enter this decrease as a positive number.
The Correct Answer and Explanation is:
To convert the temperature decrease from Fahrenheit to Celsius, we can use the following formula: ΔC=59×ΔF\Delta C = \frac{5}{9} \times \Delta FΔC=95×ΔF
Where:
- ΔC\Delta CΔC is the temperature change in Celsius.
- ΔF\Delta FΔF is the temperature change in Fahrenheit.
Given that the temperature decrease is 42.5°F, we substitute that into the formula: ΔC=59×42.5=23.61∘C\Delta C = \frac{5}{9} \times 42.5 = 23.61^\circ CΔC=95×42.5=23.61∘C
Thus, a temperature decrease of 42.5°F corresponds to a decrease of approximately 23.61°C.
Explanation:
To understand the conversion, it’s essential to note that the Fahrenheit and Celsius scales have different zero points and increments. The Fahrenheit scale has 180 intervals between the freezing and boiling points of water, whereas the Celsius scale has 100 intervals over the same temperature range. Therefore, the conversion factor between Fahrenheit and Celsius is 59\frac{5}{9}95, which accounts for the different scale sizes.
In this case, we’re looking at a decrease in temperature, so the calculated value represents the same numerical value as the Fahrenheit decrease, but in Celsius.
The formula itself is derived from the relationship between the freezing points of water in both scales: 32°F corresponds to 0°C. By using the factor 59\frac{5}{9}95, we adjust the Fahrenheit temperature change to fit the Celsius scale.
Therefore, a temperature drop of 42.5°F results in a drop of 23.61°C
