Problem 72 - Algebra and Trigonometry Real Mathematics, Real People

Question

The average July 2013 temperature in the contiguous United States was \(74.3^{\circ} \mathrm{F}\). What was the average temperature in degrees Celsius?

Step-by-Step Solution

Answer

The average temperature in degrees Celsius was approximately \(23.5^{\circ} C.\)

Step 1: Identification

Identify that the problem here is a conversion problem, specifically a Fahrenheit to Celsius conversion.

Step 2: Apply the Conversion Formula

Apply the formula \(C = (F - 32) \times \frac{5}{9}\) to the given Fahrenheit temperature \(74.3^{\circ} F\).

Step 3: Calculate

Replace \(F\) in the formula with \(74.3^{\circ} F\) and calculate the Celsius temperature: \(C = (74.3 - 32) \times \frac{5}{9} = 23.5^{\circ} C\).

Key Concepts

Temperature Conversion

Understanding temperature conversion is crucial for comparing climate data, cooking, and science experiments. It allows us to translate temperatures from the Fahrenheit scale, commonly used in the United States, to the Celsius scale, prevalent in most other countries.

In the example provided, converting the average July temperature in the United States to Celsius makes the data comprehendible in a global context. Conversions are necessary because temperature scales differ in the point set for freezing and boiling of water. In Fahrenheit, water freezes at 32 degrees and boils at 212 degrees, while in Celsius, the freezing and boiling points are 0 degrees and 100 degrees, respectively.

Learning how to switch between these scales enables us to understand weather forecasts, recipes, and scientific measurements no matter the originating country's standard.

Conversion Formula

Understanding the Formula

The conversion formula from Fahrenheit to Celsius is a simple mathematical equation: \(C = (F - 32) \times \frac{5}{9}\).

The '32' in the formula represents the difference in the freezing point of water between the two scales. The fraction \(\frac{5}{9}\) is the ratio of each Fahrenheit degree's worth compared to a degree on the Celsius scale.

Let's demonstrate the conversion with the given temperature of \(74.3^{\text{°}}F\). First, you subtract 32 from the Fahrenheit value: \(74.3 - 32 = 42.3\). Then, you multiply this result by the fraction to get the Celsius value: \(42.3 \times \frac{5}{9} \approx 23.5^{\text{°}}C\). This stepwise approach shows how the formula works and gives us the final result.

Unit Conversion

The concept of unit conversion is a foundation not just in temperature measurements, but across various fields such as length, volume, and mass.

Understanding unit conversions allows us to adapt and communicate information in the most appropriate unit for the context. It's a multi-step process that usually involves a conversion factor—an agreed-upon number used to multiply or divide the starting value to successfully convert it to the new unit.

Whether in engineering, medicine, or daily life, unit conversions are vital. The key is to know the correct conversion factor, much like the \(\frac{5}{9}\) for temperature, and apply it accurately to ensure proper communication and comprehension across different systems of measurement.