The formula used to convert degrees Celsius to degrees Fahrenheit is F=C+32.
Convert 59°F to degrees Celsius. Solve the formula for C, and then use it to convert the temperature.
Which is the correct formula and conversion?
A. C=F-32; conversion: 59°F = 135°C
B. C= (F-32); conversion: 59°F = 15°C
C. C= (F-32); conversion: 59°F = 106°C
D. C=F-32; conversion: 59°F = 15°C
The Correct Answer and Explanation is:
To convert a temperature from Fahrenheit to Celsius, we use the correct formula:
[
C = \frac{(F – 32)}{1.8}
]
Explanation and Steps for Conversion:
To solve for Celsius (C), we start by recognizing that the initial formula given, ( F = 1.8 \times C + 32 ), is typically used to convert Celsius to Fahrenheit. Here, however, we need to do the reverse: convert Fahrenheit to Celsius. Therefore, we’ll isolate ( C ) by rearranging the equation.
Starting with:
[
F = 1.8 \times C + 32
]
we subtract 32 from both sides:
[
F – 32 = 1.8 \times C
]
Next, we divide by 1.8 to isolate ( C ):
[
C = \frac{(F – 32)}{1.8}
]
Now, with ( F = 59^\circ F ), we substitute 59 for ( F ) in the formula to find ( C ):
[
C = \frac{(59 – 32)}{1.8}
]
Calculating inside the parentheses first:
[
59 – 32 = 27
]
Then, dividing by 1.8:
[
C = \frac{27}{1.8} = 15^\circ C
]
Correct Answer and Analysis
The correct answer is therefore:
D. ( C = F – 32; ) conversion: ( 59^\circ F = 15^\circ C )
Why Other Options Are Incorrect
- Option A: This answer incorrectly states that ( 59^\circ F ) converts to ( 135^\circ C ). This result is mathematically inaccurate and much higher than the expected conversion result.
- Option B and Option C: Both state ( C = (F – 32) ), which is missing the division by 1.8. Simply subtracting 32 without dividing by 1.8 does not yield the correct Celsius temperature, leading to incorrect conversions.
- Explanation of the Factor 1.8: The factor 1.8 is crucial because Fahrenheit degrees are smaller than Celsius degrees, with the Fahrenheit scale spanning 180 degrees between freezing and boiling points of water, compared to 100 degrees for Celsius. Thus, dividing by 1.8 aligns the scales accurately for conversions.
In conclusion, understanding and applying the correct formula ensures accurate temperature conversions between Fahrenheit and Celsius, as seen in option D with a final answer of ( 15^\circ C ).