Questions: A moderate fever for an otherwise healthy adult is 99 °F. Convert this temperature to degrees Celsius. Be sure your answer has the correct number of significant digits.

A moderate fever for an otherwise healthy adult is 99 °F. Convert this temperature to degrees Celsius. Be sure your answer has the correct number of significant digits.
Transcript text: A moderate fever for an otherwise healthy adult is $99 .{ }^{\circ} \mathrm{F}$. Convert this temperature to degrees Celsius. Be sure your answer has the correct number of significant digits. $\square$ ${ }^{\circ} \mathrm{C}$ $\square$ no
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Solution

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Solution Steps

Step 1: Understand the Conversion Formula

To convert a temperature from degrees Fahrenheit (\(^{\circ}F\)) to degrees Celsius (\(^{\circ}C\)), we use the formula:

\[ ^{\circ}C = \frac{5}{9} \times (^{\circ}F - 32) \]

Step 2: Substitute the Given Temperature

Substitute the given temperature of \(99^{\circ}F\) into the formula:

\[ ^{\circ}C = \frac{5}{9} \times (99 - 32) \]

Step 3: Perform the Calculation

First, calculate the difference:

\[ 99 - 32 = 67 \]

Next, multiply by \(\frac{5}{9}\):

\[ ^{\circ}C = \frac{5}{9} \times 67 \approx 37.2222 \]

Step 4: Round to the Correct Number of Significant Digits

The original temperature \(99^{\circ}F\) has two significant digits, so we round the Celsius temperature to two significant digits:

\[ ^{\circ}C \approx 37.22 \]

Final Answer

\[ \boxed{37.22^{\circ}C} \]

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