Question

A recipe for apple pie calls for a preheated \(350^{\circ} \mathrm{F}\) (three significant figures) oven. Express this temperature setting in \({ }^{\circ} \mathrm{C}\) and in \(\mathrm{K}\).

Short answer

Question: Convert the temperature setting of 350°F to Celsius and Kelvin. Answer: The temperature setting of 350°F can be expressed as 177°C in Celsius and 450K in Kelvin.

Step-by-step solution

Convert from Fahrenheit to Celsius

First, we need to convert \(350^{\circ}\mathrm{F}\) to Celsius using the formula: \({ }^{\circ}\mathrm{C} =\dfrac{5}{9}( { }^{\circ}\mathrm{F}-32)\) Plug in the given temperature, \(350^{\circ}\mathrm{F}\), into the formula: \({ }^{\circ}\mathrm{C} =\dfrac{5}{9}( 350^{\circ}\mathrm{F}-32)\) Next, perform the subtraction and multiplication: \({ }^{\circ}\mathrm{C} =\dfrac{5}{9}( 318)\) \({ }^{\circ}\mathrm{C} = 177\) Since we have three significant figures, the Celsius temperature should be expressed as: \(177^{\circ}\mathrm{C}\)

Convert from Celsius to Kelvin

Now, we need to convert \(177^{\circ}\mathrm{C}\) to Kelvin using the formula: \(\mathrm{K} = { }^{\circ}\mathrm{C} + 273.15\) Plug in the calculated Celsius temperature, \(177^{\circ}\mathrm{C}\), into the formula: \(\mathrm{K} = 177^{\circ}\mathrm{C} + 273.15\) Next, perform the addition: \(\mathrm{K} = 450.15\) Since we have three significant figures, the Kelvin temperature should be expressed as: \(450\mathrm{K}\) So, the temperature setting of \(350^{\circ}\mathrm{F}\) can be expressed as \(177^{\circ}\mathrm{C}\) in Celsius and \(450\mathrm{K}\) in Kelvin.