Convert 100 degrees Fahrenheit to Celsius using \( C = \frac{5}{9}(F - 32) \).

To convert 100 degrees Fahrenheit to Celsius using the formula ( C = \frac{5}{9}(F - 32) ), we substitute ( F ) with 100.

First, perform the subtraction in the parentheses:

[

F - 32 = 100 - 32 = 68

]

Next, we multiply this result by ( \frac{5}{9} ):

[

C = \frac{5}{9}(68)

]

Now, calculate ( \frac{5}{9} \times 68 ):

[

C = \frac{5 \times 68}{9} = \frac{340}{9}

]

Finally, divide 340 by 9 to get the Celsius temperature:

[

C \approx 37.78

]

Thus, converting 100 degrees Fahrenheit yields approximately 37.78 degrees Celsius, confirming that the correct answer is indeed 37.78°. This conversion is a standard method used in temperature conversion and highlights the relationship between the two scales based on their defined equations.