Convert 82.5 °C to temperature in degrees Fahrenheit.
a. 28.1 F
b. 124.7 F
c. 180.5°F
d. 196.3 °F
e. 356 °F
The correct answer and explanation is :
To convert 82.5°C to Fahrenheit, we use the formula:
[
F = \left( \frac{9}{5} \times C \right) + 32
]
Where:
- ( F ) is the temperature in degrees Fahrenheit
- ( C ) is the temperature in degrees Celsius
In this case, the temperature is 82.5°C. Plugging the value into the formula:
[
F = \left( \frac{9}{5} \times 82.5 \right) + 32
]
Step-by-step, we can calculate it:
- First, multiply ( 9 ) by ( 82.5 ):
[
9 \times 82.5 = 742.5
]
- Then divide ( 742.5 ) by ( 5 ):
[
742.5 \div 5 = 148.5
]
- Finally, add 32 to ( 148.5 ):
[
148.5 + 32 = 180.5
]
Thus, the temperature in Fahrenheit is 180.5°F.
Explanation:
The conversion from Celsius to Fahrenheit is linear, meaning there is a consistent relationship between the two temperature scales. The formula itself has two parts: the first part, ( \frac{9}{5} ), adjusts the magnitude of the temperature because the degree increments are larger in Fahrenheit than Celsius. The second part, ( +32 ), accounts for the different starting points of the two scales. The freezing point of water in Celsius is 0°C, whereas in Fahrenheit, it is 32°F.
By multiplying the Celsius value by ( \frac{9}{5} ), we scale the Celsius temperature to match the Fahrenheit degree increment. Adding 32 accounts for the offset between the two scales, as mentioned.
Therefore, when we convert 82.5°C, we get 180.5°F, which corresponds to answer c. 180.5°F.