# How do you convert 180° F to Celsius?

Mar 29, 2016

approximately ${82.22}^{\circ} C$

#### Explanation:

To convert from Fahrenheit to Celsius, use the formula:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {T}_{\circ C} = \left({T}_{\circ F} - 32\right) \times \frac{5}{9} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Substitute ${T}_{\circ F}$ as $180$ and solve for ${T}_{\circ C}$.

${T}_{\circ C} = \left({T}_{\circ F} - 32\right) \times \frac{5}{9}$

${T}_{\circ C} = \left(180 - 32\right) \times \frac{5}{9}$

${T}_{\circ C} = 148 \times \frac{5}{9}$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {T}_{\circ C} \approx {82.22}^{\circ} C \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Jul 18, 2017

${180}^{\circ} \text{F" = 82.bar(2)^@"C}$

#### Explanation:

The "standard" way of converting from Fahrenheit to Celsius is:

• Subtract $32$

• Multiply by $\frac{5}{9}$

So in our example:

$\left(180 - 32\right) \cdot \frac{5}{9} = 148 \cdot \frac{5}{9} = \frac{740}{9} = 82. \overline{2}$

Conversely, to convert Celsius to Fahrenheit, reverse this process:

• Multiply by $\frac{9}{5} \text{ }$ (equivalent to dividing by $\frac{5}{9}$)

• Add $32$

So if we were starting with $82. {\overline{2}}^{\circ} C$, we would find:

$\left(82. \overline{2} \cdot \frac{9}{5}\right) + 32 = \left(\frac{740}{5}\right) + 32 = 148 + 32 = 180$

Alternatively, note that $- {40}^{\circ} F = - {40}^{\circ} C$, so we can convert from Fahrenheit to Celsius by the following steps:

• Add $40$

• Multiply by $\frac{5}{9}$

• Subtract $40$

Then we find:

$\left(180 + 40\right) \cdot \frac{5}{9} - 40 = 220 \cdot \frac{5}{9} - 40 = \frac{1100}{9} - 40 = 122. \overline{2} - 40 = 82. \overline{2}$

Similarly, we can convert Celsius to Fahrenheit by:

• Add $40$

• Multiply by $\frac{9}{5}$

• Subtract $40$

So:

$\left(82. \overline{2} + 40\right) \cdot \frac{9}{5} - 40 = 122. \overline{2} \cdot \frac{9}{5} - 40 = \frac{1100}{5} - 40 = 220 - 40 = 180$