Questions: A cake is baked at 330 °F, Convert this temperature to °C. Be sure your answer has the correct number of significant figures.

A cake is baked at 330 °F, Convert this temperature to °C. Be sure your answer has the correct number of significant figures.
Transcript text: A cake is baked at $330 .{ }^{\circ} \mathrm{F}$, Convert this temperature to ${ }^{\circ} \mathrm{C}$. Be sure your answer has the correct number of significant figures.
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Solution

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Solution Steps

Step 1: Understand the Conversion Formula

To convert a temperature from Fahrenheit (\(^{\circ} \mathrm{F}\)) to Celsius (\(^{\circ} \mathrm{C}\)), we use the following formula: \[ ^{\circ} \mathrm{C} = \frac{5}{9} (^{\circ} \mathrm{F} - 32) \]

Step 2: Substitute the Given Temperature

Given the temperature is \(330 \, ^{\circ} \mathrm{F}\), we substitute this value into the formula: \[ ^{\circ} \mathrm{C} = \frac{5}{9} (330 - 32) \]

Step 3: Perform the Calculation

First, calculate the difference: \[ 330 - 32 = 298 \]

Next, multiply by \(\frac{5}{9}\): \[ ^{\circ} \mathrm{C} = \frac{5}{9} \times 298 \approx 165.5556 \]

Step 4: Round to the Correct Number of Significant Figures

The given temperature \(330 \, ^{\circ} \mathrm{F}\) has three significant figures. Therefore, we should round the Celsius temperature to three significant figures as well: \[ 165.5556 \approx 165.6 \]

Final Answer

\[ \boxed{165.6 \, ^{\circ} \mathrm{C}} \]

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