Question

What is 120 degrees Fahrenheit in Celsius?

Answer 1

Hint: We solve this problem using the scale conversions of temperatures. The standard formula for conversion of Fahrenheit to Celsius or Celsius to Fahrenheit is given as,
${\displaystyle \frac{C-0}{100-0}}={\displaystyle \frac{F-32}{212-32}}$
Where, ${}^{\prime }{C}^{\prime }$ is the temperature in Celsius scale and ${}^{\prime }{F}^{\prime }$ is the temperature in Fahrenheit scale.
By using the above formula and given temperature in a respected scale we can find the temperature in another scale.

Complete step-by-step solution:
We are given that the temperature in the Fahrenheit is 120 degrees.
Let us assume that the given temperature in Fahrenheit scale as,
$\Rightarrow F=120$
We are asked to find the temperature in Celsius scale.
So, let us assume that the required temperature in Celsius scale as ${}^{\prime }{C}^{\prime }$
We know that the standard formula for conversion of Fahrenheit to Celsius or Celsius to Fahrenheit is given as,
${\displaystyle \frac{C-0}{100-0}}={\displaystyle \frac{F-32}{212-32}}$
Where, ${}^{\prime }{C}^{\prime }$ is the temperature in Celsius scale and ${}^{\prime }{F}^{\prime }$ is the temperature in Fahrenheit scale.
Now, by using the above formula for the given temperature then we get,
$$\begin{array}{rl}& \Rightarrow {\displaystyle \frac{C-0}{100-0}}={\displaystyle \frac{120-32}{212-32}}\\ & \Rightarrow {\displaystyle \frac{C}{100}}={\displaystyle \frac{88}{180}}\end{array}$$
Now, by cross multiplying the terms from LHS to RHS then we get,
$\begin{array}{rl}& \Rightarrow C={\displaystyle \frac{88}{180}}\times 100\\ & \Rightarrow C={48.89}^{\circ }C\end{array}$
Therefore, we can conclude that the 120 degrees Fahrenheit is equal to 48.89 degrees Celsius that is,
$\therefore {120}^{\circ }F={48.89}^{\circ }C$

Note: We have the direct steps to find out the required temperature in Celsius scale if the given temperature is in Fahrenheit as follows,
(i) Subtract 32 from the given temperature of Fahrenheit scale.
(ii) Multiply the result in (i) with ${\displaystyle \frac{5}{9}}$
Now, let us use the above steps to find the required answer.
We are given that the temperature in the Fahrenheit is 120 degrees.
Let us assume that the given temperature in Fahrenheit scale as,
$\Rightarrow F=120$
Let us assume the result in step (i) as ${}^{\prime }{X}^{\prime }$
Now, by applying the first step we get,
$\begin{array}{rl}& \Rightarrow X=120-32\\ & \Rightarrow X=88\end{array}$
So, let us assume that the result in step (ii) which is the required temperature in Celsius scale as ${}^{\prime }{C}^{\prime }$
By applying the second step then we get,
$\begin{array}{rl}& \Rightarrow C=88\times {\displaystyle \frac{5}{9}}\\ & \Rightarrow C=48.89\end{array}$
Therefore, we can conclude that the 120 degrees Fahrenheit is equal to 48.89 degrees Celsius that is,
$\therefore {120}^{\circ }F={48.89}^{\circ }C$