A thermometer gives a reading of $96.1^{\circ} \mathrm{F} \pm 0.2^{\circ} \mathrm{F}\( . What is the temperature in \)^{\circ} \mathrm{C} ?$ What is the uncertainty?

Short Answer

Expert verified
The temperature in Celsius is \(35.61^{\circ}\mathrm{C} \pm 0.11^{\circ}\mathrm{C}\).

Step by step solution

01

Identify the conversion formula

We need to use the conversion formula between Fahrenheit and Celsius, which is given by: \[C = \frac{5}{9}(F - 32)\] Where \(C\) is the temperature in Celsius, and \(F\) is the temperature in Fahrenheit.
02

Convert the given temperature

Using the formula, replace the \(F\) with the given Fahrenheit temperature \(96.1^{\circ}\mathrm{F}\): \(C = \frac{5}{9}(96.1 - 32)\) Now, calculate the result: \(C = \frac{5}{9}(64.1) = 35.61^{\circ}\mathrm{C}\) So, the temperature in Celsius is \(35.61^{\circ}\mathrm{C}\).
03

Convert the uncertainty

To determine the uncertainty in Celsius, treat the uncertainty as a separate temperature and use the same conversion formula: \(\Delta C = \frac{5}{9}(- 0.2^{\circ}\mathrm{F})\) Calculate the result: \(\Delta C = \frac{5}{9}(-0.2) = -0.11^{\circ}\mathrm{C}\) By convention, we always express the uncertainty as a positive value, so the uncertainty in Celsius is \(0.11^{\circ}\mathrm{C}\).
04

Write the final answer

Combine the converted temperature and its uncertainty in Celsius: The temperature in Celsius is \(35.61^{\circ}\mathrm{C} \pm 0.11^{\circ}\mathrm{C}\).

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