Questions: Air temperature on an extreme winter day is -65 °F. Convert this temperature to °C. Be sure your answer has the correct number of significant figures.

Solution Steps

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

Substitute the given temperature in Fahrenheit (-65 °F) into the formula: \[ °C = \frac{5}{9} (-65 - 32) \]

First, simplify the expression inside the parentheses: \[ -65 - 32 = -97 \] Then, multiply by \(\frac{5}{9}\): \[ °C = \frac{5}{9} \times (-97) \]

Calculate the multiplication: \[ °C = \frac{5 \times -97}{9} = \frac{-485}{9} \approx -53.8889 \]

Since the original temperature (-65 °F) has two significant figures, the converted temperature should also have two significant figures: \[ °C \approx -53.89 \]

Final Answer