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.) A medication contains a crystalline substance with a melting point of about \(186^{\circ} \mathrm{C}\) _______ \({ }^{\circ} \mathrm{F}\)

Short answer

The equivalent is 366.8°F.

Step-by-step solution

Understand the Conversion Formula

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

Plug in the Given Temperature

We have \( 186^{\circ} \mathrm{C} \). Substitute \( C = 186 \) into the formula: \[ F = 186 \times \frac{9}{5} + 32 \].

Calculate the Multiplication

Calculate the multiplication part of the formula: \( 186 \times \frac{9}{5} = 334.8 \).

Add to Complete the Conversion

Add 32 to the result from the previous step to complete the conversion: \( 334.8 + 32 = 366.8 \).

Round to the Nearest Tenth

Round 366.8 to the nearest tenth, which remains 366.8.

Key concepts

Celsius to Fahrenheit Conversion

Converting temperatures from Celsius to Fahrenheit is vital for understanding various scientific and everyday contexts. The formula for this conversion is: \[ F = C \times \frac{9}{5} + 32 \] where \( F \) represents the temperature in Fahrenheit, and \( C \) is the temperature in Celsius. This calculation requires multiplying the Celsius value by \( \frac{9}{5} \), converting the Celsius measurement into a comparable scale to Fahrenheit. After multiplying, we add 32 to account for the offset in the zero point between the two scales. This simple two-step process can convert any Celsius temperature directly into Fahrenheit, allowing for practical applications like adjusting to weather reports or scientific data conversion. By understanding and applying this conversion formula, one can effectively bridge the gap between different temperature scales.

Numerical Problem-Solving

Successfully solving numerical problems involves more than just carrying out calculations; it requires logical thinking and a systematic approach. For instance, with our temperature conversion example, it is important to:

• Understand what the problem is asking (convert \( 186^{\circ} \mathrm{C} \) to Fahrenheit).
• Identify and apply the correct formula for the task.
• Perform each step carefully while checking for potential errors.
• Round the result to the required precision if necessary.

Breaking down the problem into smaller steps simplifies the process, and ensures accuracy. Approaching a problem with these strategies can enhance one's ability to navigate and solve a range of numerical issues in both academic and real-world settings.

Mathematical Calculations

Accurate calculations are the backbone of correct answers in many fields, including temperature conversion. Let’s delve into the specific steps of our conversion problem:First, multiply the Celsius temperature by \( \frac{9}{5} \). For \( 186^{\circ} \mathrm{C} \), this means calculating: \[ 186 \times \frac{9}{5} = 334.8 \] This multiplication converts the Celsius value into a scale that aligns with Fahrenheit measurements.Next, add 32 to 334.8, resulting in: \[ 334.8 + 32 = 366.8 \] This addition accounts for the differences in the starting point of the Celsius and Fahrenheit scales. Finally, round the result if needed to ensure it's suitable for the context provided, like medication melting points which might require a high degree of precision. Careful attention to detail in each step ensures accuracy and reliability in the outcome.

Pharmaceutical Calculations

In the pharmaceutical field, precise temperature knowledge is crucial. Substances may have specific melting points, crucial when considering medication formulation and stability. Our example involved converting a melting point from Celsius to Fahrenheit for a pharmaceutical context. Accurate temperature conversion aids in ensuring proper storage and efficacy of pharmaceuticals. High precision in these calculations can prevent potential errors in drug formulation. It’s also essential to understand and communicate these temperatures adequately between global teams who might use different temperature units. Pharmacists and healthcare professionals must often perform such conversions to ensure drugs maintain their potency and safety under varying conditions, highlighting the practical application and importance of these mathematical skills in the field.