Question

To convert temperature in \[^0F\] into \[^0C\] we use the formula
A. \[\dfrac{F}{{100}} = \dfrac{{C - 32}}{{180}}\]
B. \[C = \dfrac{5}{9}\left( {F - 32} \right)\]
C. \[F = \dfrac{5}{9}\left( {C - 32} \right)\]
D. \[C = \dfrac{9}{5}\left( {F - 32} \right)\]

Answer 1

Hint: As the formula for the conversion of \[^0F\] into \[^0C\] is \[\dfrac{{C - 0}}{{100}} = \dfrac{{F - 32}}{{180}}\], we can obtain our answer by applying simple math applications like multiplications on both sides. So, use this concept to reach the solution of the given problem.

Complete step-by-step answer:
Here we have to convert \[^0F\] into \[^0C\].
We know that to convert \[^0F\] into \[^0C\] we use the formula
\[\dfrac{{C - 0}}{{100}} = \dfrac{{F - 32}}{{180}}\]
Multiplying both sides with 20, we have
\[
  \dfrac{{C - 0}}{{100}} \times 20 = \dfrac{{F - 32}}{{180}} \times 20 \\
  \dfrac{C}{5} = \dfrac{{F - 32}}{9} \\
\]
Now, multiplying both sides with 5 we have
\[
  \dfrac{C}{5} \times 5 = \dfrac{{F - 32}}{9} \times 5 \\
  \therefore C = \dfrac{5}{9}\left( {F - 32} \right) \\
\]
Thus, the correct option is B. \[C = \dfrac{5}{9}\left( {F - 32} \right)\]

Note: The Fahrenheit scale and Celsius scale are used to measure the degree of temperature. The formula for the direct conversion from \[^0C\] into \[^0F\] is given by \[F = \dfrac{9}{5}C + 32\].