## Converting Between Fahrenheit and Celsius Temperatures

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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.

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

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

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

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

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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