In the metric system of weights and measures, temperature is measured in degrees Celsius (°C) instead of degrees Fahrenheit (°F). To convert between the two systems, we use the equations. C =5/9 (F-32) and F = 9/5C+32. In each exercise, convert to the other system. Round answers to the nearest tenth of a degree if necessary. 100°F

Verified step by step guidance

1. Identify the given temperature and the system it is in. Here, the temperature is 100°F, which is in degrees Fahrenheit.
2. Since the temperature is given in Fahrenheit and we need to convert it to Celsius, use the conversion formula: \(C = \frac{5}{9} (F - 32)\).
3. Substitute the given Fahrenheit value into the formula: \(C = \frac{5}{9} (100 - 32)\).
4. Simplify the expression inside the parentheses: calculate \$100 - 32$.
5. Multiply the result by \(\frac{5}{9}\) to find the temperature in degrees Celsius, then round to the nearest tenth if necessary.

Key Concepts

Linear Equations and Formulas

The temperature conversion between Fahrenheit and Celsius is based on linear equations that relate the two scales. Understanding how to manipulate and apply these formulas, such as C = (5/9)(F - 32) and F = (9/5)C + 32, is essential for converting temperatures accurately.

Order of Operations and Arithmetic

Correctly applying the order of operations (parentheses, multiplication, addition/subtraction) is crucial when substituting values into the conversion formulas. This ensures accurate calculation of the temperature in the target unit.

Rounding and Significant Figures

After performing the conversion, rounding the result to the nearest tenth is necessary to match the problem's requirements. Understanding how to round decimals properly helps present the final answer clearly and correctly.