Question

For each of the following statements, change the given temperature to its corresponding equivalent in \({ }^{\circ} \mathrm{C}\) or \({ }^{\circ} \mathrm{F}\). (Round to the nearest tenth.) An infant has a body temperature of \(36.5^{\circ} \mathrm{C}\). _______ \({ }^{\circ} \mathrm{F}\)

Short answer

The infant's temperature is 97.7°F.

Step-by-step solution

Identify the Formula

To convert a temperature from Celsius to Fahrenheit, we use the formula: \( F = \left( \frac{9}{5} \right) C + 32 \).

Substitute the Given Celsius Temperature

Substitute \( C = 36.5 \) into the formula: \( F = \left( \frac{9}{5} \right) \times 36.5 + 32 \).

Perform the Multiplication

First, multiply \( 36.5 \) by \( \frac{9}{5} \). Calculate \( 36.5 \times \frac{9}{5} = 36.5 \times 1.8 = 65.7 \).

Add 32 to the Result

Add 32 to the product from Step 3: \( 65.7 + 32 = 97.7 \).

Round to the Nearest Tenth

The calculated Fahrenheit temperature is already at one decimal place, so it is \( 97.7^{\circ} \mathrm{F} \).

Key concepts

Celsius to Fahrenheit

Converting temperatures between Celsius and Fahrenheit is quite common, especially when trying to compare weather data, or when handling recipes and scientific data. To assist with this conversion, a specific formula is used to accurately move from one scale to the other. The two scales are based on different points at which water freezes and boils, with Celsius putting freezing at 0°C and boiling at 100°C. Meanwhile, Fahrenheit places the freezing point at 32°F and the boiling at 212°F. This difference necessitates a specific conversion to translate from one to the other.

When you convert a temperature from Celsius to Fahrenheit, it’s a useful skill that can help in many everyday situations. This conversion is particularly common in countries that use Celsius for weather forecasts and scientific measurements, providing results that resonate with international standards or those familiar with Fahrenheit.

conversion formula

The conversion process relies on a mathematical formula that directly ties Celsius (\(C\)) to Fahrenheit (\(F\)). This formula is given by:
\[F = \left( \frac{9}{5} \right) C + 32\]

Here’s how it breaks down:

• The fraction \(\frac{9}{5}\) adjusts for the difference in scale between Celsius and Fahrenheit.
• Multiplying this fraction by the Celsius temperature multiplies the proportion.
• Adding 32 to the result transitions the scale to begin at the Fahrenheit freezing point.

By carefully inserting the Celsius value into this equation, you can find its Fahrenheit equivalent. This process ensures accuracy and allows even conversion across a range of temperatures.

step-by-step solution

To solidify your understanding of the conversion from Celsius to Fahrenheit, consider this step-by-step guide:

**Identify the Formula**
First, know the formula: \(F = \left( \frac{9}{5} \right) C + 32\). This is your conversion tool.

**Substitute the Given Temperature**
Say you have a temperature of 36.5°C (like in our example with the infant's body temperature). Replace \(C\) with 36.5:
\[F = \left( \frac{9}{5} \right) \times 36.5 + 32\]

**Perform the Multiplication**
Next, carry out the multiplication:

• Multiply 36.5 by 1.8 (since \(\frac{9}{5} = 1.8\)).
• This results in 65.7.

**Add 32 to the Result**
Now, simply add 32 to the previous result:
\[65.7 + 32 = 97.7\]

**Round Off as Necessary**
Round to one decimal place if needed. In this instance, 97.7°F is already set with the decimal in place.

Using these clear steps helps ensure that the conversion is not only accurate but also easily replicated in any instance where Celsius to Fahrenheit conversion is needed.