Question

A toddler in Italy visits the family doctor. The nurse takes the child's temperature, which reads \(38.8^{\circ} \mathrm{C}\). (a) Convert this temperature to \({ }^{\circ} \mathrm{F}\). (b) If \(98.6^{\circ} \mathrm{F}\) is considered normal, does the child have a fever?

Short answer

The child's temperature in Fahrenheit is \(101.84^{\circ}\mathrm{F}\). Yes, the child has a fever.

Step-by-step solution

- Understand the Conversion Formula

To convert Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5}C + 32 \].

- Plug in the given Celsius temperature

The child’s temperature in Celsius is given as \(38.8^{\circ}\mathrm{C}\). Plug this value into the formula: \[ F = \frac{9}{5}(38.8) + 32 \].

- Perform the multiplication

First, multiply \(38.8\) by \(\frac{9}{5}\): \[ \frac{9}{5} \times 38.8 = 69.84 \].

- Add 32 to the result

Now, add 32 to \(69.84\): \[ 69.84 + 32 = 101.84^{\circ}\mathrm{F} \].

- Evaluate if the child has a fever

\(98.6^{\circ}\mathrm{F}\) is considered normal. Since \(101.84^{\circ}\mathrm{F}\) is higher than \(98.6^{\circ}\mathrm{F}\), the child has a fever.

Key concepts

Celsius to Fahrenheit conversion

Converting temperatures from Celsius (\textdegree C) to Fahrenheit (\textdegree F) is essential in both everyday life and various scientific fields, including chemistry. The formula to make this conversion is straightforward: \ \ \ \ \ \[ F = \frac{9}{5}C + 32 \]. \ Breaking it down step by step: \ \ \ \ \ \ In the formula, \( C \) represents the temperature in Celsius, \ while \( F \) represents the temperature in Fahrenheit. \ First, multiply the Celsius temperature by \( \frac{9}{5} \). \ Then, add 32 to the result. \ This will give you the temperature in Fahrenheit. \ For example, to convert \ \( 38.8^{\textdegree}C \) to Fahrenheit: \ 1. Multiply \( 38.8 \) by \( \frac{9}{5} \), which equals \( 69.84 \). \ 2. Add 32 to \( 69.84 \), resulting in \( 101.84^{\textdegree}F \). \ This mathematical transformation is crucial for interpreting temperature readings across different regions and contexts.

fever detection

Detecting a fever involves taking a person's body temperature and comparing it to normal ranges. \ A 'normal' temperature for a healthy individual is typically around \( 98.6^{\textdegree}F \) (37\textdegree C). \ When a temperature exceeds this threshold, particularly if it goes above \( 100.4^{\textdegree}F \) (38\textdegree C), it can indicate a fever. \ In the exercise above, a child's temperature was converted from \( 38.8^{\textdegree}C \) to \( 101.84^{\textdegree}F \). \ Since \( 101.84^{\textdegree}F \) is above the normal threshold, it strongly suggests that the child has a fever. \ Recognizing fever is important for diagnosing and responding to potential health issues.

temperature calculation steps

Accurate temperature calculation involves following clear steps to ensure correctness: \ 1. **Understand the Conversion Formula:** \ The formula for converting Celsius to Fahrenheit is simple: \ \( F = \frac{9}{5} C + 32 \). \ 2. **Substitute the Given Temperature:** \ Plug the given Celsius value into the formula. \ In this case, \ \( 38.8^{\textdegree}C \) is substituted. \ 3. **Perform Multiplication First:** \ Multiply \ \( 38.8 \) by \ \( \frac{9}{5} \), which results in \ \( 69.84 \). \ 4. **Add the Constant:** \ Add 32 to \ \( 69.84 \) to get \ \( 101.84^{\textdegree}F \). \ 5. **Evaluate the Result for Fever:** \ Compare the calculated temperature (\textdegree F) with the normal threshold (98.6\textdegree F). \ If it exceeds this value, assess fever presence. \ This step-by-step approach ensures that temperature conversions are precise and meaningful for clinical interpretations.