Answer :
Sure, let's solve the problem step-by-step to convert [tex]\(116^\circ F\)[/tex] to Celsius using the formula [tex]\(C = \frac{5}{9}(F - 32)\)[/tex].
1. Write down the formula:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
2. Substitute the given Fahrenheit temperature (116°F) into the formula:
[tex]\[
C = \frac{5}{9}(116 - 32)
\][/tex]
3. Calculate the value inside the parentheses:
[tex]\[
116 - 32 = 84
\][/tex]
4. Substitute 84 back into the equation:
[tex]\[
C = \frac{5}{9} \times 84
\][/tex]
5. Multiply [tex]\(\frac{5}{9}\)[/tex] by 84:
[tex]\[
C = \frac{5 \times 84}{9} = \frac{420}{9} \approx 46.66666666666667
\][/tex]
6. Round the result to one decimal place:
[tex]\[
46.66666666666667 \approx 46.7
\][/tex]
So, if the temperature is [tex]\(116^\circ F\)[/tex], that is equivalent to [tex]\(46.7^\circ C\)[/tex].
Hence, the temperature in degrees Celsius is [tex]\(46.7^\circ C\)[/tex].
1. Write down the formula:
[tex]\[
C = \frac{5}{9}(F - 32)
\][/tex]
2. Substitute the given Fahrenheit temperature (116°F) into the formula:
[tex]\[
C = \frac{5}{9}(116 - 32)
\][/tex]
3. Calculate the value inside the parentheses:
[tex]\[
116 - 32 = 84
\][/tex]
4. Substitute 84 back into the equation:
[tex]\[
C = \frac{5}{9} \times 84
\][/tex]
5. Multiply [tex]\(\frac{5}{9}\)[/tex] by 84:
[tex]\[
C = \frac{5 \times 84}{9} = \frac{420}{9} \approx 46.66666666666667
\][/tex]
6. Round the result to one decimal place:
[tex]\[
46.66666666666667 \approx 46.7
\][/tex]
So, if the temperature is [tex]\(116^\circ F\)[/tex], that is equivalent to [tex]\(46.7^\circ C\)[/tex].
Hence, the temperature in degrees Celsius is [tex]\(46.7^\circ C\)[/tex].
