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. \(F=-4^{\circ}\)

Short answer

The Celsius temperature is -20°C.

Step-by-step solution

- Understand the Given Formula

The formula given for converting Fahrenheit to Celsius is \[C = \frac{5}{9}(F-32)\]. This means we need to substitute the given Fahrenheit value into this formula to find the corresponding Celsius value.

- Substitute the Fahrenheit Value

Substitute the given Fahrenheit temperature \( F = -4 \) into the formula. This gives us \[C = \frac{5}{9}(-4-32)\].

- Simplify the Expression

First, calculate the expression inside the parentheses: \(-4 - 32 = -36\). Now our formula looks like \[C = \frac{5}{9}(-36)\].

- Calculate the Final Value

Multiply \( \frac{5}{9} \) by \(-36\): \[ \frac{5}{9} \times -36 = \frac{5 \times -36}{9} = \frac{-180}{9} = -20 \]. Thus, the Celsius temperature is \[ C = -20 \].

Key concepts

Celsius

Celsius, also known as centigrade, is a scale and unit of measurement for temperature. It is widely used around the world, especially in science. The Celsius scale is named after the Swedish astronomer Anders Celsius. The Celsius temperature scale is based on the freezing point of water at 0 degrees and the boiling point of water at 100 degrees, both under standard atmospheric conditions. This scale is linear, meaning the difference between degrees is consistent across the scale.

Fahrenheit

The Fahrenheit scale is a temperature measurement system primarily used in the United States and a few other countries. It was developed by Daniel Gabriel Fahrenheit, a Polish-German physicist, in the early 18th century. On the Fahrenheit scale, the freezing point of water is 32 degrees, and the boiling point of water is 212 degrees. This scale is less intuitive than the Celsius scale, but it remains in regular use for daily weather forecasts and household thermometers.

Conversion Formula

The conversion formula to change a temperature from Fahrenheit to Celsius is \[ C = \frac{5}{9}(F-32) \]This formula subtracts 32 from the Fahrenheit temperature, which adjusts the base reference point to zero degrees Celsius. Then, multiplying by \( \frac{5}{9} \) scales the measurement from the wider range of Fahrenheit to the narrower range of Celsius. This formula is essential for converting temperatures first accurately and simply.

Algebra Steps

To convert a given Fahrenheit temperature to Celsius, follow these algebraic steps:

• Step 1: Plug the Fahrenheit temperature into the conversion formula. For example, if \( F = -4 \), then \[ C = \frac{5}{9}(-4-32) \]
• Step 2: Calculate the value inside the parentheses. Here, \( -4 - 32 = -36 \). Substitute this back into the formula to get \[ C = \frac{5}{9}(-36) \]
• Step 3: Multiply \( \frac{5}{9} \) by \( -36 \): \[ \frac{5}{9} \times -36 = \frac{-180}{9} = -20 \]
• Step 4: The final result is that \( C = -20 \). This is your converted temperature from Fahrenheit to Celsius.

Following these steps will help you accurately convert any temperature from Fahrenheit to Celsius using basic algebra.