Question

Use the formula \(C=\frac{5}{9}(F-32)\) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. \(F=212^{\circ}\)

Short answer

100°C

Step-by-step solution

Identify the given value

The given temperature in Fahrenheit is \( F = 212^{\circ} \)

Write down the conversion formula

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

Substitute the Fahrenheit value into the formula

Replace \( F \) with \( 212 \) in the formula: \( C = \frac{5}{9}(212 - 32) \)

Simplify the expression inside the parentheses

Calculate the value inside the parentheses: \( 212 - 32 = 180 \)

Perform the multiplication

Multiply the result by \( \frac{5}{9} \): \[ C = \frac{5}{9} \times 180 \]

Simplify the final expression

Carry out the multiplication: \( C = \frac{900}{9} = 100 \)

State the final answer

The temperature in Celsius is \( C = 100^{\circ} \)

Key concepts

temperature conversion formula

Understanding how to convert temperatures from one scale to another is very useful. One popular formula you might encounter is the temperature conversion formula. The equation for converting degrees Fahrenheit to degrees Celsius is: \ (C = \frac{5}{9}(F - 32))\. This formula allows you to determine the equivalent Celsius temperature when you have a temperature given in Fahrenheit.

This formula relies on two operations:

• First, subtracting 32 from the Fahrenheit temperature.
• Second, multiplying that result by \(\frac{5}{9}\).

If you remember these two operations, converting between Fahrenheit and Celsius will become much easier.

Understanding why the formula works can deepen your comprehension. The difference in the two scales’ starting points and the size of one-degree increments are accounted for by subtracting 32 and multiplying by \(\frac{5}{9}\) respectively.

degrees Fahrenheit

Degrees Fahrenheit, often denoted with the symbol \(F\), is a unit of measurement for temperature primarily used in the United States and some Caribbean countries. The Fahrenheit scale was developed by Daniel Gabriel Fahrenheit. On this scale:

• The freezing point of water is 32 degrees Fahrenheit.
• The boiling point of water is 212 degrees Fahrenheit.

To visualize how this scale works, remember that between the freezing and boiling points of water, there are 180 degrees Fahrenheit. This scale is less commonly used globally, but understanding it is crucial for interpreting temperatures in various countries that still use this system.

degrees Celsius

Degrees Celsius, abbreviated as \(C\), is a temperature measurement unit used across most of the world, including Europe and Asia. This scale was developed by Anders Celsius. In this system:

• The freezing point of water is 0 degrees Celsius.
• The boiling point of water is 100 degrees Celsius.

A key feature of the Celsius scale is that it is based on the properties of water and makes use of a 100-degree interval between the freezing and boiling points of water. Knowing the Celsius equivalent of common Fahrenheit temperatures can be useful, especially if you are in a science-related field or traveling internationally.

step-by-step solution

To ensure you fully grasp how to convert Fahrenheit to Celsius, here is a detailed step-by-step solution using the provided exercise where Fahrenheit is 212 degrees:

Step 1: Identify the given value. You know that the temperature in Fahrenheit is \(F = 212^{\circ}\).

Step 2: Write down the conversion formula. Use \(C = \frac{5}{9}(F - 32)\).

Step 3: Substitute the Fahrenheit value into the formula. Replace \(F\) with 212 in the formula:
\(C = \frac{5}{9}(212 - 32)\).

Step 4: Simplify the expression inside the parentheses. Calculate \(212 - 32 = 180\).

Step 5: Perform the multiplication. Multiply the result by \(\frac{5}{9}\): \[ C = \frac{5}{9} \times 180 \].

Step 6: Simplify the final expression. Carry out the multiplication:
\(C = \frac{900}{9} = 100^{\circ}\).

Step 7: State the final answer. The temperature in Celsius is 100 degrees.