Question

Convert \[{{36}^{\circ }}C\] into \[^{\circ }F\] by using conversion of units of temperature.

Answer 1

Hint: In this type of question we have to use the concept of measuring units of temperature. We know that for measuring temperature Fahrenheit and Celsius are two widely used scales. We know that, the temperature in the Fahrenheit scale is represented as degree Fahrenheit and the temperature in the Celsius scale is represented as degree Celsius. Also we know that the scales Fahrenheit and Celsius are directly proportional to each other. We use the units \[^{\circ }C\] to denote the Celsius scale and \[^{\circ }F\] to denote the Fahrenheit scale.

Complete step by step answer:
Now, we have to convert \[{{36}^{\circ }}C\] into \[^{\circ }F\] by using the conversion of units of temperature.
For this we consider the relationship between the units of temperature i.e. the relationship between the scales Fahrenheit and Celsius.
We know that the scales Fahrenheit and Celsius are directly proportional to each other.
For converting the scale of temperature from Celsius to Fahrenheit, we will use the following formula:
\[\Rightarrow F=\left( \dfrac{9}{5}\times C \right)+32\]
Where \[F\] refers to the temperature in Fahrenheit, and \[C\] refers to the temperature in Celsius scale.
For converting the scale of temperature from Fahrenheit to Celsius, we will use the following formula:
\[\Rightarrow C=\dfrac{5}{9}\times \left( F-32 \right)\]
Where \[F\] refers to the temperature in Fahrenheit, and \[C\] refers to the temperature in Celsius scale.
Now let us convert \[{{36}^{\circ }}C\] into \[^{\circ }F\]
For converting \[{{36}^{\circ }}C\] into \[^{\circ }F\], we have to use the formula,
\[\Rightarrow F=\left( \dfrac{9}{5}\times C \right)+32\]
Where \[F\] refers to the temperature in Fahrenheit, and \[C\] refers to the temperature in Celsius scale.
Here, the value of \[C\] is \[{{36}^{\circ }}C\]. So we will substitute the value of \[C\] in above formula to obtain the value of \[F\]
\[\begin{align}
  & \Rightarrow F=\left( \dfrac{9}{5}\times 36 \right)+32 \\
 & \Rightarrow F={{96.8}^{\circ }}F \\
\end{align}\]
Hence, \[{{36}^{\circ }}C={{96.8}^{\circ }}F\]

Note: In this type of question students have to remember the formulas for conversion of temperature from Celsius to Fahrenheit as well as from Fahrenheit to Celsius. Students have to take care and should not get confused in the conversion formulas. Also students have to note that both the Celsius and Fahrenheit scales have their respective thermometer for measurements.