Convert 65°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas.
The Correct Answer and Explanation is:
To convert 65°F to degrees Celsius, we use the formula provided: C=59(F−32)C = \frac{5}{9}(F – 32)
Substitute F=65F = 65: C=59(65−32)=59×33C = \frac{5}{9}(65 – 32) = \frac{5}{9} \times 33 C=1659≈18.333…C = \frac{165}{9} \approx 18.333…
Rounded to the nearest tenth of a degree: C≈18.3∘CC \approx \boxed{18.3^\circ \text{C}}
Explanation
Temperature conversion between Fahrenheit and Celsius is a common need in science, travel, and daily life, especially because the United States uses Fahrenheit while most of the world uses Celsius. Understanding the conversion formula helps interpret temperatures accurately in different units.
The Fahrenheit and Celsius scales are both used to measure temperature, but they are based on different reference points. The Celsius scale is based on the freezing point of water at 0°C and the boiling point at 100°C. The Fahrenheit scale sets the freezing point of water at 32°F and the boiling point at 212°F.
To convert from Fahrenheit (°F) to Celsius (°C), we use the formula: C=59(F−32)C = \frac{5}{9}(F – 32)
This formula subtracts 32 from the Fahrenheit temperature (to account for the offset of freezing point on the Fahrenheit scale) and then scales the result by 5/9 to convert to the Celsius scale.
In the problem above, the given temperature is 65°F. Substituting into the formula gives: C=59(65−32)=59×33=1659≈18.3∘CC = \frac{5}{9}(65 – 32) = \frac{5}{9} \times 33 = \frac{165}{9} \approx 18.3^\circ C
We are asked to round to the nearest tenth, which is one digit after the decimal point. Since the number is 18.333…, we round it to 18.3.
Thus, 65°F is equivalent to 18.3°C, making it a mild and comfortable room temperature.
