Problem 72 - Prealgebra

Question

In the metric system, the scale we use to measure temperature is the Celsius scale. On this scale water boils at 100 degrees and freezes at 0 degrees. When we write 100 degrees measured on the Celsius scale, we use the notation \(100^{\circ} \mathrm{C},\) which is read "100 degrees Celsius." If we know the temperature in degrees Fahrenheit, we can convert to degrees Celsius by using the formula $$c=\frac{5(F-32)}{9}$$ where \(F\) is the temperature in degrees Fahrenheit. Use this formula to find the temperature in degrees Celsius for each of the following Fahrenheit temperatures. \(32^{\circ} \mathrm{F}\)

Step-by-Step Solution

Answer

The temperature in Celsius is \(0^{\circ} \mathrm{C}\).

Step 1: Identify the Known Value

We are given the temperature in Fahrenheit, which is \(32^{\circ} \mathrm{F}\).

Step 2: Understand the Conversion Formula

The formula to convert Fahrenheit (\(F\)) to Celsius (\(c\)) is \(c = \frac{5(F-32)}{9}\).

Step 3: Substitute the Known Value

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

Step 4: Simplify the Equation

Perform the subtraction inside the parentheses: \(32 - 32 = 0\). Thus, the equation becomes \(c = \frac{5 \times 0}{9}\).

Step 5: Calculate the Result

Multiply and divide the remaining values: \(\frac{5 \times 0}{9} = 0\). So, \(c = 0^{\circ} \mathrm{C}\).

Key Concepts

Metric System

The metric system is a convenient and logically structured system of measurement used worldwide. It is especially popular in the field of science and in countries outside the United States. One of its greatest strengths is the ease with which conversions can be made between units. This is because it predominantly uses powers of ten to relate different units.
For example, in the metric system, the unit used for measuring temperature is the Celsius scale. Celsius is preferred in many countries due to its straightforward reference points: water boils at 100 degrees and freezes at 0 degrees Celsius. This makes it easy to remember and practical for everyday use.
Countries using the metric system find it easier to communicate scientific data without needing to worry about conversion errors or misunderstandings. Using Celsius as a unit of temperature measurement is one example of how the metric system helps streamline communication in a universally understood way.

Temperature Measurement

Temperature is an essential aspect of daily life and scientific research. It provides a quantitative way to describe how hot or cold an object is. The Celsius and Fahrenheit scales are two temperature measurement systems we commonly encounter.
The Celsius scale is based on the freezing and boiling points of water, making it practical and intuitive. When water turns into ice at 0 degrees Celsius and boils at 100 degrees Celsius, it creates a clear framework for understanding temperature changes.
In contrast, the Fahrenheit scale, used primarily in the United States, sets the freezing point of water at 32 degrees and the boiling point at 212 degrees. While not as rounded as the Celsius scale, it is equally precise. Understanding both scales and how to convert between them is helpful, especially for global communications and scientific endeavors.

Mathematical Formulas

Mathematical formulas are crucial tools in converting temperatures from one scale to another. They are precise equations that help translate a known temperature into another unit, making them hugely valuable in scientific studies and daily life.
For converting Fahrenheit to Celsius, the formula used is \(c = \frac{5(F-32)}{9}\). This equation breaks down into clear steps for conversion:

• First, subtract 32 from the given Fahrenheit temperature.
• Next, multiply the result by 5.
• Finally, divide the obtained product by 9 to get the equivalent Celsius temperature.

Such formulas require careful steps to ensure accurate conversion, and practicing these can solidify understanding of the relationship between different temperature scales. They also exemplify how mathematical principles apply to everyday tasks, such as adjusting to the metric system when traveling or studying abroad.