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Question 5, 7.3.39

Convert to Celsius. Use [tex]C=\frac{5}{9}(F-32)[/tex] or [tex]F=\frac{9}{5}C+32[/tex], where [tex]F[/tex] is the degrees in Fahrenheit and [tex]C[/tex] is the degrees in Celsius.

[tex]
\begin{array}{r}
-16^{\circ} F \\
-16^{\circ} F =
\end{array}
[/tex]

[tex]
{ }^{\circ} C
[/tex]

(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.)



Answer :

GinnyAnswer
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.

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