Sure, let's convert the given temperature from Fahrenheit to Celsius using the provided formula for the conversion:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
Here, [tex]\( F \)[/tex] is the degrees in Fahrenheit, and [tex]\( C \)[/tex] is the degrees in Celsius.
Given that [tex]\( F = 11 \)[/tex], we can plug this value into the formula:
1. Subtract 32 from the Fahrenheit temperature:
[tex]\[
F - 32 = 11 - 32 = -21
\][/tex]
2. Multiply the result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[
C = \frac{5}{9} \times (-21)
\][/tex]
3. Perform the multiplication:
[tex]\[
C = \frac{5}{9} \times (-21) = -\frac{105}{9} \approx -11.666666666666668
\][/tex]
So, the temperature in Celsius before rounding is approximately:
[tex]\[ C \approx -11.666666666666668 \][/tex]
4. Round to the nearest tenth:
[tex]\[
C \approx -11.7
\][/tex]
Therefore, [tex]\( 11^{\circ} F \)[/tex] converts to [tex]\(\boxed{-11.7^{\circ} C}\)[/tex] when rounded to the nearest tenth.
