Question

Your friend who is visiting from Canada just took her temperature. When she reads \(99.8{ }^{\circ} \mathrm{F}\), she becomes concerned that she is quite ill. How would you explain this temperature to your friend?

Short answer

The temperature of 99.8°F converts to 37.67°C, indicating a mild fever.

Step-by-step solution

- Understand the Problem

Your friend measured her body temperature in Fahrenheit. She is concerned about her health based on this measurement. You need to convert the temperature to Celsius to help her understand if the temperature is high.

- Use the Fahrenheit to Celsius Conversion Formula

The formula to convert temperature from Fahrenheit to Celsius is: \[ C = \frac{5}{9} (F - 32) \]Here, \( F \) is the temperature in Fahrenheit, and \( C \) will be the temperature in Celsius.

- Substitute the Given Temperature

Substitute \( F = 99.8 \) into the conversion formula:\[ C = \frac{5}{9} (99.8 - 32) \]

- Perform the Calculation

First, calculate the difference:\[ 99.8 - 32 = 67.8 \]Next, multiply by 5/9:\[ C = \frac{5}{9} \times 67.8 \]\[ C = 37.67 \]

- Interpret the Result

A temperature of 37.67°C is only slightly above the normal body temperature, which is about 37°C. This means your friend does have a mild fever, but it's not extremely high.

Key concepts

Fahrenheit to Celsius formula

To help your friend understand her temperature, we need to convert it from Fahrenheit to Celsius. This is because many people in different parts of the world use Celsius to measure temperature, including regions in Canada.

The formula to convert Fahrenheit to Celsius is simple:
\[ C = \frac{5}{9} (F - 32) \]
Here, \(F\) represents the temperature in Fahrenheit, and \(C\) will be the temperature in Celsius.

By using this equation, we can understand temperature measurements better and compare them with standard body temperature values to determine if someone might have a fever.

body temperature

Understanding body temperature is crucial for assessing health. The normal body temperature for a healthy person ranges around 37°C (98.6°F).

However, this can slightly vary based on several factors, including the time of day and the method of measurement. For instance:

• Oral measurements slightly differ from ear or forehead measurements.
• Body temperature tends to be lower in the morning and higher in the late afternoon and evening.

When using the Fahrenheit to Celsius conversion, identifying small Celsius differences becomes easier. For instance, a reading of 37.67°C (or 99.8°F) is just a bit above the standard 37°C, indicating a rise that might be considered mild fever.

Knowing these subtle differences helps decide if medical attention is necessary.

fever definition

A fever indicates that your body is fighting an infection or illness. Medically, a fever is typically defined as a body temperature above the average normal range.

In Celsius, that often means over 38°C (100.4°F) for an adult. Here's a quick summary of what different temperature ranges might mean:

• Normal: around 37°C (98.6°F)
• Low-grade fever: 37.1°C to 38°C (98.7°F to 100.4°F)
• High-grade fever: anything above 38°C (100.4°F)

Based on this, your friend's temperature of 37.67°C (99.8°F) suggests a low-grade fever. While it’s not alarmingly high, it's a sign her body could be responding to something unusual. She should rest, stay hydrated, and consult a healthcare provider if necessary.