A nurse has to record her temperatures in Celsius but her thermometer reads Fahrenheit. A patient's temperature is 100.7° F. What is the temperature in °C?

1. Break Down the Problem

To convert the temperature from Fahrenheit (°F) to Celsius (°C), we'll use the conversion formula: $C = \frac{5}{9} (F - 32)$ where $C$ is the temperature in Celsius and $F$ is the temperature in Fahrenheit.

2. Relevant Concepts

The formula provided allows us to accurately convert temperatures from Fahrenheit to Celsius. It is critical to note the constants involved in the conversion and the order of operations.

3. Analysis and Detail

1. Start with the given temperature in Fahrenheit: $F = 100.7$
2. Substitute $F$ into the conversion equation: $C = \frac{5}{9} (100.7 - 32)$
3. Perform the subtraction: $100.7 - 32 = 68.7$
4. Now substitute this result back into the equation: $C = \frac{5}{9} \times 68.7$
5. Multiply to find $C$: $C = \frac{5 \times 68.7}{9} \approx \frac{343.5}{9} \approx 38.22$

4. Verify and Summarize

We calculated $C \approx 38.22$. This conversion can be checked by reversing the process:

1. Convert $38.22$ back to Fahrenheit: $F = \frac{9}{5} \times C + 32$ $F = \frac{9}{5} \times 38.22 + 32 \approx 100.696 \, \text{°F}$ This value is approximately the original $100.7 \, \text{°F}$, confirming the conversion was performed correctly.

Final Answer

The temperature in Celsius is approximately $38.22 \, \text{°C}$.