Question

Express the following Fahrenheit temperatures in degrees Celsius: (a) \(101^{\circ} \mathrm{F}\) (b) \(-215^{\circ} \mathrm{F}\)

Short answer

(a) 101°F ≈ 38.33°C; (b) -215°F ≈ -137.22°C.

Step-by-step solution

Understanding the Conversion Formula

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

Convert 101°F to Celsius

For part (a), substitute \( F = 101 \) into the formula:\[ C = \frac{5}{9} (101 - 32) \]Calculate:1. \( 101 - 32 = 69 \)2. \( \frac{5}{9} \times 69 \approx 38.33 \)So, \( 101^{\circ} \mathrm{F} \) is approximately \( 38.33^{\circ} \mathrm{C} \).

Convert -215°F to Celsius

For part (b), substitute \( F = -215 \) into the formula:\[ C = \frac{5}{9} (-215 - 32) \]Calculate:1. \( -215 - 32 = -247 \)2. \( \frac{5}{9} \times (-247) \approx -137.22 \)So, \( -215^{\circ} \mathrm{F} \) is approximately \( -137.22^{\circ} \mathrm{C} \).

Key concepts

Celsius to Fahrenheit conversion

Temperature conversion is a common task in science and everyday life. Understanding how to convert between Celsius and Fahrenheit is essential for interpreting weather forecasts, cooking recipes, and academic exercises. To convert Celsius to Fahrenheit, you apply a straightforward formula: The formula to convert Celsius to Fahrenheit is: \[ F = \frac{9}{5}C + 32 \] Where:

• \( F \) represents the temperature in Fahrenheit.
• \( C \) represents the temperature in Celsius.

This formula tells us that the temperature in Fahrenheit is computed by multiplying the Celsius temperature by 9/5 and then adding 32. This reflects the different starting points (0°C vs 32°F) and the size of each increment (1°C vs 1.8°F). By using this formula, you can easily transform temperatures from the metric system to the imperial system, making it practical to convert between them for various applications.

Fahrenheit to Celsius formula

The reverse process, converting Fahrenheit to Celsius, is equally important and involves a slightly different formula. This conversion is essential for many scientific applications, especially in regions where Fahrenheit is commonly used, like the United States. The formula for Fahrenheit to Celsius conversion is: \[ C = \frac{5}{9}(F - 32) \] Breaking it down:

• Subtract 32 from the Fahrenheit temperature to "neutralize" the Fahrenheit offset.
• Then, multiply the result by 5/9 to scale it to Celsius units.

This formula helps recalibrate the Fahrenheit temperature into a Celsius context, acknowledging both the zero-point offset of 32 degrees Fahrenheit and the larger numerical scale used in the Fahrenheit scale.

Temperature calculation steps

Calculating temperature conversions involves a simple yet structured approach. Once you know the right formula, the steps are easy to follow and repeatable for any conversion task. Let's break down the calculation steps for converting temperatures from Fahrenheit to Celsius using examples. **Step 1: Identify and apply the formula.** First, recall the formula: \[ C = \frac{5}{9}(F - 32) \] This formula will serve as your roadmap. **Step 2: Substitute known values into the formula.**For example, if you want to convert 101°F to Celsius, substitute \( F = 101 \) into the formula: \[ C = \frac{5}{9}(101 - 32) \] **Step 3: Perform the arithmetic calculations.**

• Calculate 101 - 32, which equals 69.
• Multiply 69 by \( \frac{5}{9} \), getting approximately 38.33°C.

Apply the same steps for another example like \( -215^{\circ} \mathrm{F} \), inserting \( F = -215 \): \[ C = \frac{5}{9}(-215 - 32) \] Calculate

• -215 - 32 equals -247.
• Multiply -247 by \( \frac{5}{9} \), receiving about -137.22°C.

These methodical steps simplify the conversion process, ensuring accuracy and understanding for each calculation task, no matter the starting temperature.