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.

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.
Transcript text: 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.
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Solution

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Solution Steps

Step 1: Identify the Formula

To convert a temperature from Fahrenheit (°F) to Celsius (°C), we use the formula: °C=59(°F32) °C = \frac{5}{9} (°F - 32)

Step 2: Substitute the Given Value

Substitute the given temperature in Fahrenheit (-65 °F) into the formula: °C=59(6532) °C = \frac{5}{9} (-65 - 32)

Step 3: Simplify the Expression

First, simplify the expression inside the parentheses: 6532=97 -65 - 32 = -97 Then, multiply by 59\frac{5}{9}: °C=59×(97) °C = \frac{5}{9} \times (-97)

Step 4: Perform the Calculation

Calculate the multiplication: °C=5×979=485953.8889 °C = \frac{5 \times -97}{9} = \frac{-485}{9} \approx -53.8889

Step 5: Round to the Correct Number of Significant Figures

Since the original temperature (-65 °F) has two significant figures, the converted temperature should also have two significant figures: °C53.89 °C \approx -53.89

Final Answer

53.89°C \boxed{-53.89 \, °C}

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