Question

a. A patient with hyperthermia has a temperature of \(106^{\circ} \mathrm{F}\). What does this read on a Celsius thermometer? b. Because high fevers can cause convulsions in children, the doctor wants to be called if the child's temperature goes over \(40.0^{\circ} \mathrm{C}\). Should the doctor be called if a child has a temperature of \(103^{\circ} \mathrm{F}\) ?

Short answer

a. 106°F ≈ 41.1°C. b. 103°F ≈ 39.4°C, so the doctor should not be called.

Step-by-step solution

Convert Fahrenheit to Celsius for part a

To convert a temperature from Fahrenheit (\text{F}) to Celsius (\text{C}), use the formula: \[ C = \frac{5}{9} (F - 32) \]For a temperature of 106°F: \[ C = \frac{5}{9} (106 - 32) \] \[ C = \frac{5}{9} \times 74 \] \[ C \approx 41.1^{\circ} \text{C} \]

Evaluate if the doctor should be called for part b

Convert 103°F to Celsius using the same formula: \[ C = \frac{5}{9} (103 - 32) \] \[ C = \frac{5}{9} \times 71 \] \[ C \approx 39.4^{\circ} \text{C} \]The temperature 39.4°C is below 40.0°C, so the doctor should not be called.

Key concepts

Fahrenheit to Celsius Conversion

Temperature conversion is a basic yet very important skill, especially in medical contexts. Fahrenheit (°F) and Celsius (°C) are two different scales to measure temperature. To convert a temperature from Fahrenheit to Celsius, you can use the formula: \( C = \frac{5}{9} (F - 32) \)
In this formula, you subtract 32 from the Fahrenheit temperature, then multiply the result by five-ninths.
For example, to convert 106°F to Celsius:
\( C = \frac{5}{9} (106 - 32) \)
\( C = \frac{5}{9} \times 74 \)
\( C \approx 41.1^{\circ} \text{C} \)
This shows that a temperature of 106°F is approximately 41.1°C.
This formula is essential for understanding temperature in various contexts, especially in medicine, where specific temperature thresholds must be maintained or noted.

Hyperthermia

Hyperthermia is a medical condition where the body temperature is significantly higher than normal.
Normal body temperature is around 98.6°F (37°C).
Hyperthermia occurs when the body temperature rises above 100.4°F (38°C).
It is different from fever, which is usually caused by an infection.
Hyperthermia can occur due to heat stroke, prolonged exposure to the sun, or strenuous exercise.
When someone has a body temperature of 106°F (41.1°C), they are experiencing severe hyperthermia.
This condition is very dangerous and requires immediate medical attention.
Symptoms of hyperthermia can include:

• Hot and dry skin
• Increased heart rate
• Confusion or dizziness
• Nausea or vomiting

Severe cases can lead to loss of consciousness or even death if not treated promptly.

Temperature Thresholds in Medical Contexts

In medical settings, certain temperature thresholds signify critical conditions that require different responses.
For instance, high fevers in children can cause convulsions.
Doctors usually want to be alerted if a child’s fever exceeds 40.0°C (104.0°F).
From the previous example, if we convert a child's temperature of 103°F to Celsius:
\( C = \frac{5}{9} (103 - 32) \)
\( C \approx 39.4^{\circ} \text{C} \)
The temperature of 39.4°C is below the 40.0°C threshold, indicating that the doctor may not need to be called.
Understanding these thresholds helps in making prompt medical decisions.
Regular monitoring and accurate conversion between temperature scales are crucial for effective healthcare management.