To convert a temperature from Fahrenheit to Celsius, we use the formula:
[tex]\[ C = \frac{5}{9} (F - 32) \][/tex]
where [tex]\( F \)[/tex] is the temperature in degrees Fahrenheit, and [tex]\( C \)[/tex] will be the temperature in degrees Celsius.
Given [tex]\( F = -16^\circ \text{F} \)[/tex], we substitute this value into the formula:
[tex]\[ C = \frac{5}{9} (-16 - 32) \][/tex]
First, calculate the expression inside the parentheses:
[tex]\[ -16 - 32 = -48 \][/tex]
Next, multiply this result by [tex]\(\frac{5}{9}\)[/tex]:
[tex]\[ C = \frac{5}{9} \times -48 \][/tex]
Perform the multiplication:
[tex]\[ C = \frac{5 \times -48}{9} = \frac{-240}{9} \approx -26.666666666666668 \][/tex]
So, the temperature in degrees Celsius before rounding is approximately [tex]\(-26.666666666666668^\circ \text{C}\)[/tex].
Now, we round this value to the nearest tenth:
[tex]\[ -26.666666666666668 \approx -26.7 \][/tex]
Thus, [tex]\(-16^\circ \text{F}\)[/tex] is approximately [tex]\(-26.7^\circ \text{C}\)[/tex] when rounded to the nearest tenth.
