Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(106^{\circ} \mathrm{C}=\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

\(106^{\circ} \mathrm{C}\) is approximately \(222.8^{\circ} \mathrm{F}\).

Step-by-step solution

Understand the conversion formula

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

Substitute the Celsius value

Substitute the given Celsius temperature \( 106^{\circ} \mathrm{C} \) into the formula. This gives: \( F = \frac{9}{5} \times 106 + 32 \).

Perform the multiplication

Calculate \( \frac{9}{5} \times 106 \). This equals \( 190.8 \).

Add 32

Now add 32 to the result from the previous step: \( 190.8 + 32 = 222.8 \).

Round to the nearest tenth

The result is already at the nearest tenth, \( 222.8 \). Thus, the temperature in Fahrenheit is approximately \( 222.8^{\circ} \mathrm{F} \).

Key concepts

Celsius to Fahrenheit

Converting temperatures from Celsius to Fahrenheit is a common task in science and everyday life. This conversion allows us to understand temperature measurements across different systems used around the world. The Celsius scale is often used in most of the world, whereas the Fahrenheit scale is primarily used in the United States. It's essential to correctly convert these values for accurate scientific computations or when planning daily activities like cooking or dressing appropriately in different regions. The key to successful conversion lies in using the correct formula and understanding each component. By converting these temperatures correctly, you broaden your ability to interpret data and make informed decisions in both travel and international contexts.

Conversion Formula

The formula for converting Celsius to Fahrenheit is straightforward yet powerful: \[ F = \frac{9}{5}C + 32 \]In this equation:

• The variable \(C\) stands for the Celsius temperature you want to convert.
• The expression \(\frac{9}{5}\) is the ratio that adjusts for the difference in scale between Fahrenheit and Celsius. This multiplier effectively scales the degrees in Celsius to match the Fahrenheit system.
• Adding 32 accounts for the fact that the two systems have different starting points, with the freezing point of water being 0°C and 32°F.

This formula is crucial for scrupulous conversion and ensures precision in interpreting temperatures. Moreover, keeping the order of operations in mind while computing these calculations ensures that results are accurate.

Rounding Numbers

Rounding numbers is the process of adjusting a figure to a specified degree of accuracy, often to make them simpler to work with while retaining as much useful information as necessary. When converting measurements like temperature, rounding to the nearest tenth can heighten accuracy without excess precision. The general rule for rounding is:

• If the digit is 5 or greater, round up.
• If the digit is less than 5, round down.

In our example, after converting 106°C to Fahrenheit, we reached a result of 222.8°F. This number is conveniently already rounded to one decimal place, illustrating a perfect application of the rounding principle. Keeping temperatures rounded to the nearest tenth balances clarity and precision, which is especially helpful when dealing with practical applications where overly precise values are unnecessary.