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Converting Between Fahrenheit and Celsius Temperatures

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Converting Between Fahrenheit and Celsius Temperatures

Have you ever been in a foreign country and heard the weather forecast? If the forecast is for \(22\text{°C}.\) What does that mean?

The U.S. and metric systems use different scales to measure temperature. The U.S. system uses degrees Fahrenheit, written \(\text{°F}.\) The metric system uses degrees Celsius, written \(\text{°C}.\) The figure below shows the relationship between the two systems.

Converting Between Fahrenheit and Celsius Temperatures

A temperature of \(37\text{°C}\) is equivalent to \(98.6\text{°F}.\)

If we know the temperature in one system, we can use a formula to convert it to the other system.

Definition: Temperature Conversion

To convert from Fahrenheit temperature, \(\text{F},\) to Celsius temperature, \(\text{C},\) use the formula

\(C=\frac{5}{9}\left(F-32\right)\)

To convert from Celsius temperature, \(\text{C},\) to Fahrenheit temperature, \(\text{F},\) use the formula

\(F=\frac{9}{5}C+32\)

Optional Video: Convert from Celsius to Fahrenheit

Example

Convert \(50\text{°F}\) into degrees Celsius.

Solution

We will substitute \(50\text{°F}\) into the formula to find \(\text{C}.\)

Use the formula for converting °F to °C\(C=\frac{5}{9}\left(F-32\right)\)
Converting Between Fahrenheit and Celsius TemperaturesConverting Between Fahrenheit and Celsius Temperatures
Simplify in parentheses.\(C=\frac{5}{9}\left(18\right)\)
Multiply.\(C=10\)
 A temperature of 50°F is equivalent to 10°C.

Example

The weather forecast for Paris predicts a high of \(20\text{°C.}\) Convert the temperature into degrees Fahrenheit.

Solution

We will substitute \(20\text{°C}\) into the formula to find \(\text{F}.\)

 
Use the formula for converting °F to °C\(F=\frac{9}{5}C+32\)
Converting Between Fahrenheit and Celsius TemperaturesConverting Between Fahrenheit and Celsius Temperatures
Multiply.\(F=36+32\)
Add.\(F=68\)
 So 20°C is equivalent to 68°F.

Optional Video: Convert from Fahrenheit to Celsius

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