Question

For each of the following statements, change the given temperature to its corresponding equivalent in \({ }^{\circ} \mathrm{C}\) or \({ }^{\circ} \mathrm{F}\). (Round to the nearest tenth.) Store medication at room temperature, \(77^{\circ} \mathrm{F}\) _______ \({ }^{\circ} \mathrm{C}\)

Short answer

The equivalent temperature is \( 25^{\circ} \mathrm{C} \).

Step-by-step solution

Understand the formula

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

Substitute the value

Substitute the given Fahrenheit temperature (\( 77^{\circ} \mathrm{F} \)) into the formula:\[ C = \frac{5}{9} (77 - 32) \].

Perform the subtraction

First calculate the expression inside the parenthesis:\( 77 - 32 = 45 \).

Multiply and divide

Now calculate the fraction:\[ C = \frac{5}{9} \times 45 \]. First, multiply 45 by 5:\( 45 \times 5 = 225 \).

Final division calculation

Divide 225 by 9 to get the Celsius temperature:\( 225 \div 9 = 25 \). So, the equivalent temperature in Celsius is \( 25^{\circ} \mathrm{C} \).

Key concepts

Fahrenheit to Celsius

Temperature conversion is a common task in various scientific and everyday applications. To convert a temperature from Fahrenheit to Celsius, you can use a specific mathematical formula. Understanding this formula not only helps in specific tasks like storing medication but can also be useful in a variety of contexts. A temperature given in degrees Fahrenheit can be converted to degrees Celsius using the formula:\[ C = \frac{5}{9} (F - 32) \]This equation consists of a fractional multiplication of the temperature difference (in Fahrenheit) by \( \frac{5}{9} \), which accounts for the variations between the two scales. Remember, this formula is derived from the freezing and boiling points of water, marking the point 32 for freezing and 212 for boiling in Fahrenheit, which correspond to 0 and 100 in Celsius, respectively.

Medication Storage

When discussing medication storage, temperature plays a critical role in maintaining the efficacy of many medical products. Medications often have specific storage requirements that must be adhered to in order to ensure they remain effective. Keeping medications at room temperature, which is traditionally considered to be around \(77^{\circ} \text{Fahrenheit} \), is an important guideline.The conversion of room temperature to Celsius is useful not just for precision, but also for those using the metric system, which is more widely used globally. Ensuring proper medication storage:

• Prevents degradation of active ingredients.
• Maintains stability and safety of the medication.

Knowing how to convert these values can be particularly helpful when dealing with international guidelines or instructions.

Mathematical Formula

The core component of converting Fahrenheit to Celsius is the use of a mathematical formula. This formula is not arbitrary but grounded in consistent mathematical principles. The conversion involved here relies on basic arithmetic and understanding the order of operations.The formula \( C = \frac{5}{9} (F - 32) \) is intuitively structured:- Subtraction \( (F - 32) \) captures the difference between the two scales' starting points.- The multiplication by \(\frac{5}{9}\) adjusts for the scale difference, aligning the numeric value to Celsius.Understanding this formula allows one to seamlessly convert temperatures and adjust to different measurement systems without confusion. It's an essential piece of knowledge, especially for those interested in science, cooking, travel, or any field requiring temperature precision.

Arithmetic Operations

The execution of this temperature conversion relies heavily on fundamental arithmetic operations. It involves following through a sequence of steps carefully:1. **Subtraction**: Start by calculating the difference between the Fahrenheit value and 32. For example, with \(77 \text{F}\), you calculate \(77 - 32 = 45\).2. **Multiplication**: Next, take this result and multiply by 5. This process scales down the value, moving it closer to the Celsius range. Thus, \(45 \times 5 = 225\).3. **Division**: Finally, divide by 9 to complete the transition to Celsius, arriving at \(225 \div 9 = 25\). This division scales the number to its final equivalent in the Celsius system.These steps illustrate the importance of knowing basic arithmetic principles to not just solve this problem, but many similar mathematical problems. Mastering such operations empowers one with the ability to quickly and accurately handle everyday calculations.