Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(102.8^{\circ} \mathrm{F}=\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

102.8°F is approximately 39.3°C.

Step-by-step solution

Understanding the Conversion Formula

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

Substitute Known Value

Substitute the given temperature in degrees Fahrenheit, which is 102.8, into the conversion formula:\[ C = \frac{5}{9} (102.8 - 32) \]

Perform the Subtraction

Calculate the subtraction within the formula:\[ 102.8 - 32 = 70.8 \]

Calculate the Conversion

Apply the division and multiplication in the conversion formula:\[ C = \frac{5}{9} \, \times \, 70.8 \approx 39.3333 \]

Round the Result

Round the result to the nearest tenth: Since 39.3333 rounded to the nearest tenth is 39.3, we conclude that the temperature in Celsius is 39.3° C.

Key concepts

Fahrenheit to Celsius Conversion

Temperature conversion can be a bit tricky if you don't know the right way to tackle it. Changing a Fahrenheit degree to Celsius is done through a straightforward mathematical formula. This type of conversion is especially useful in science and global communication where Celsius is commonly used. To successfully convert Fahrenheit to Celsius, you’ll need to remember a simple equation and follow some basic steps.

• Start by writing down the given temperature in Fahrenheit. This is the temperature you're converting, in our exercise, it's 102.8° F.
• Next, you use the conversion formula which provides a structured approach to find the equivalent Celsius temperature.
• Apply the formula step-by-step which simplifies the process and ensures accuracy.

Begin practicing with different numbers to get comfortable using the formula repeatedly.

Mathematical Formula for Conversion

The mathematical formula is at the heart of converting temperatures between Fahrenheit and Celsius. For anyone new to conversions, the formula might look intimidating, yet it's entirely logical. On paper, the formula reads:\[ C = \frac{5}{9} (F - 32) \]Here, \(C\) stands for Celsius, and \(F\) for Fahrenheit. It involves two main operations:

• First, by subtracting 32 from the Fahrenheit temperature, you eliminate the offset caused by Fahrenheit's strange starting point.
• Then, multipling the result by \(\frac{5}{9}\), you scale it down to match the Celsius scale.

Once you understand it, utilizing this formula makes temperature conversion a breeze!

Rounding Numbers

Not only do you need to convert temperatures, but sometimes you need to present them more simply. That's where rounding numbers comes in handy. It's about simplifying numbers while maintaining their value as closely as possible. Let’s see how to round 39.3333 to the nearest tenth:

• Look at the hundredths place, which is the second digit right after the decimal. Here it's a 3.
• If this digit is 5 or higher, you round up the tenths place. If it is lower, as in our example, you keep the tenths the same.

So, 39.3333 becomes 39.3 when rounded to the nearest tenth. Practicing rounding in various situations boosts your math skills greatly.

Educational Math

Math is an integral part of our daily lives, and understanding concepts like temperature conversion makes managing tasks easier. Educational math emphasizes breaking down complex problems into manageable steps, much like we did with converting Fahrenheit to Celsius. When learning such math problems:

• Identify the key formula or method involved. Often, these will be provided in your study materials.
• Understand each step logically instead of rote memorization.
• Practice often to instill confidence and expertise over time.

By utilizing educational strategies, conversion tasks become clearer, aiding in other mathematical queries you might encounter.