Question

Convert temperatures as indicated. Round your answer to the nearest tenth. \(64.4^{\circ} \mathrm{F}=\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

64.4°F is approximately 18.0°C.

Step-by-step solution

Recall the conversion formula

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

Substitute the Fahrenheit value

Substitute \(F = 64.4\) into the formula: \(C = \frac{5}{9} (64.4 - 32)\).

Simplify the expression inside the parentheses

Calculate \(64.4 - 32\) to get \(32.4\). Thus, the formula becomes \(C = \frac{5}{9} \times 32.4\).

Multiply and simplify

Now, calculate \(\frac{5}{9} \times 32.4\). This equals approximately \(18\). Calculate it precisely to get about \(18.0\) (since \(64.4^{\circ} \mathrm{F} \approx 18.0^{\circ} \mathrm{C}\)).

Round the answer

Round the calculated Celsius temperature to the nearest tenth. \(18.0\) is already rounded to the nearest tenth.

Key concepts

Converting Fahrenheit to Celsius

When you want to convert a temperature reading from Fahrenheit to Celsius, you're translating it into a different scale. This scale change helps to make temperature readings consistent with scientific measurements, which commonly use Celsius. Sometimes, you might need to do this conversion for school problems, recipes, or scientific data. Understanding why you need this can help make sense of the numbers you work with.
Each temperature scale has a specific starting point and degree size. The Fahrenheit scale begins at water's freezing point of 32 degrees, whereas Celsius starts at 0 degrees. Knowing these benchmarks makes it easier to understand the conversion process. Below is the formula that bridges these two scales.

The Temperature Conversion Formula

To translate a Fahrenheit temperature into Celsius, use a specific formula that's both simple and helpful:
\[ C = \frac{5}{9} (F - 32) \]
In this formula, **\(C\)** represents the temperature in Celsius, while **\(F\)** stands for the temperature in Fahrenheit. Here's a breakdown of this formula:

• Subtract 32: This represents adjusting for the zero point difference between the two scales.
• Multiply by \(\frac{5}{9}\): This corrects the difference in degree size between the two scales, where a Celsius degree is larger than a Fahrenheit degree.

By substituting a Fahrenheit value into the formula, you can find the corresponding Celsius temperature. For example, to convert 64.4°F, you simply substitute 64.4 for \(F\) in the equation, then follow the order of operations: first subtract, then multiply. This will give you the temperature in Celsius.

Rounding Temperatures

After performing the conversion calculation, you may need to round the result. Rounding ensures that the temperature is easier to read and compare. It is crucial when precision to the nearest tenth is required, especially in fields like science or cooking.
In our example, the calculated Celsius temperature was approximately 18.0, achieved by solving the equation \(C = \frac{5}{9} \times 32.4\). As it happens, 18.0 is exactly already rounded to the nearest tenth.

• Check the digits: If the digit after the tenth place is 5 or greater, round up. Otherwise, leave it the same.
• This process ensures that your temperature readings are accurate to the necessary degree.

Utilizing rounding in temperature conversions provides a neat and simplified answer that’s practical in everyday applications, ensuring you're using a consistent and understandable number.