Answer :
We begin by recalling the conversion formulas between Celsius and Fahrenheit:
[tex]$$
\text{Celsius to Fahrenheit:} \quad F = \frac{9}{5}C + 32
$$[/tex]
[tex]$$
\text{Fahrenheit to Celsius:} \quad C = \frac{5}{9}(F - 32)
$$[/tex]
Now, we will solve each row in the table step-by-step.
–––––––––––––––
Step 1. Convert 10°C to Fahrenheit:
Given the temperature is [tex]$10^\circ C$[/tex], we use the Celsius-to-Fahrenheit formula:
[tex]$$
F = \frac{9}{5}(10) + 32 = 18 + 32 = 50.0
$$[/tex]
Thus, [tex]$10^\circ C$[/tex] is equivalent to [tex]$50.0^\circ F$[/tex].
–––––––––––––––
Step 2. Convert 87°F to Celsius:
We are given [tex]$87^\circ F$[/tex], and we convert to Celsius using the Fahrenheit-to-Celsius formula:
[tex]$$
C = \frac{5}{9}(87 - 32)
$$[/tex]
First, subtract 32 from 87:
[tex]$$
87 - 32 = 55
$$[/tex]
Now, multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(55) \approx 30.6
$$[/tex]
Thus, [tex]$87^\circ F$[/tex] is approximately [tex]$30.6^\circ C$[/tex] (rounded to the nearest tenth).
–––––––––––––––
Step 3. Convert -5°C to Fahrenheit:
Using the Celsius-to-Fahrenheit formula for [tex]$-5^\circ C$[/tex]:
[tex]$$
F = \frac{9}{5}(-5) + 32 = -9 + 32 = 23.0
$$[/tex]
Thus, [tex]$-5^\circ C$[/tex] is equivalent to [tex]$23.0^\circ F$[/tex].
–––––––––––––––
Step 4. Convert 10°F to Celsius:
Given [tex]$10^\circ F$[/tex], we apply the Fahrenheit-to-Celsius formula:
[tex]$$
C = \frac{5}{9}(10 - 32)
$$[/tex]
Subtract 32 from 10:
[tex]$$
10 - 32 = -22
$$[/tex]
Now, multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(-22) \approx -12.2
$$[/tex]
Thus, [tex]$10^\circ F$[/tex] is approximately [tex]$-12.2^\circ C$[/tex].
–––––––––––––––
Summary of the completed table:
[tex]$$
\begin{array}{|c|c|}
\hline
\textbf{Degrees Celsius} & \textbf{Degrees Fahrenheit} \\
\hline
10 & 50.0 \\
\hline
30.6 & 87 \\
\hline
-5 & 23.0 \\
\hline
-12.2 & 10 \\
\hline
\end{array}
$$[/tex]
Each conversion has been rounded to the nearest tenth as required.
[tex]$$
\text{Celsius to Fahrenheit:} \quad F = \frac{9}{5}C + 32
$$[/tex]
[tex]$$
\text{Fahrenheit to Celsius:} \quad C = \frac{5}{9}(F - 32)
$$[/tex]
Now, we will solve each row in the table step-by-step.
–––––––––––––––
Step 1. Convert 10°C to Fahrenheit:
Given the temperature is [tex]$10^\circ C$[/tex], we use the Celsius-to-Fahrenheit formula:
[tex]$$
F = \frac{9}{5}(10) + 32 = 18 + 32 = 50.0
$$[/tex]
Thus, [tex]$10^\circ C$[/tex] is equivalent to [tex]$50.0^\circ F$[/tex].
–––––––––––––––
Step 2. Convert 87°F to Celsius:
We are given [tex]$87^\circ F$[/tex], and we convert to Celsius using the Fahrenheit-to-Celsius formula:
[tex]$$
C = \frac{5}{9}(87 - 32)
$$[/tex]
First, subtract 32 from 87:
[tex]$$
87 - 32 = 55
$$[/tex]
Now, multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(55) \approx 30.6
$$[/tex]
Thus, [tex]$87^\circ F$[/tex] is approximately [tex]$30.6^\circ C$[/tex] (rounded to the nearest tenth).
–––––––––––––––
Step 3. Convert -5°C to Fahrenheit:
Using the Celsius-to-Fahrenheit formula for [tex]$-5^\circ C$[/tex]:
[tex]$$
F = \frac{9}{5}(-5) + 32 = -9 + 32 = 23.0
$$[/tex]
Thus, [tex]$-5^\circ C$[/tex] is equivalent to [tex]$23.0^\circ F$[/tex].
–––––––––––––––
Step 4. Convert 10°F to Celsius:
Given [tex]$10^\circ F$[/tex], we apply the Fahrenheit-to-Celsius formula:
[tex]$$
C = \frac{5}{9}(10 - 32)
$$[/tex]
Subtract 32 from 10:
[tex]$$
10 - 32 = -22
$$[/tex]
Now, multiply by [tex]$\frac{5}{9}$[/tex]:
[tex]$$
C = \frac{5}{9}(-22) \approx -12.2
$$[/tex]
Thus, [tex]$10^\circ F$[/tex] is approximately [tex]$-12.2^\circ C$[/tex].
–––––––––––––––
Summary of the completed table:
[tex]$$
\begin{array}{|c|c|}
\hline
\textbf{Degrees Celsius} & \textbf{Degrees Fahrenheit} \\
\hline
10 & 50.0 \\
\hline
30.6 & 87 \\
\hline
-5 & 23.0 \\
\hline
-12.2 & 10 \\
\hline
\end{array}
$$[/tex]
Each conversion has been rounded to the nearest tenth as required.
