# What is 89 Fahrenheit in Celsius?

Sep 20, 2015

${32}^{\circ} \text{C}$

#### Explanation:

Celcius to Farenheit conversion

$\frac{C - 0}{100 - 0} = \frac{F - 32}{212 - 32}$

$\frac{C}{100} = \frac{89 - 32}{180}$

$C = \frac{57}{180} \cdot 100 = \frac{57}{9} \cdot 5 = \frac{95}{3} \cong {32}^{\circ} \text{C}$

Sep 20, 2015

${T}_{C} = 31.666 \ldots$ degree Celsius.

#### Explanation:

This should be in the Physics section but anyway...

For this, you need to know the formula that converts Fahrenheit to Celsius.

Googling it, you will easily find that:
${T}_{C} = \left({T}_{F} - 32\right) \cdot \frac{5}{9}$

where ${T}_{C}$ is the temperature in Celsius,
and ${T}_{F}$ is the temperature in Fahrenheit.

So, since ${T}_{F} = 89$, we have:

${T}_{C} = \left(89 - 32\right) \cdot \frac{5}{9}$
so
${T}_{C} = 57 \cdot \frac{5}{9}$

I'm sure most people would pull out their calculator at this stage, but we could simplify it a bit more, if one notices that $57 = 30 + 27 = 3 \cdot 10 + 3 \cdot 9 = 3 \cdot 19$.
Then we can simplify the 3 (because $9 = 3 \cdot 3$) and we have:
${T}_{C} = 19 \cdot \frac{5}{3}$

Then $19 \cdot 5 = 95$, and we are left with:
${T}_{C} = \frac{95}{3}$

You could bust out your calculator at this point but we could go a bit further, if one notices that $95 = 93 + 2$ where 93 is a multiple of 3.
${T}_{C} = \frac{93}{3} + \frac{2}{3}$

Since $\frac{93}{3} = 31$ and you do know that $\frac{2}{3} = 0.6666 \ldots$ (well, you must know that $\frac{1}{3} = 0.33333 \ldots$ so that $\frac{2}{3} = 0.66666 \ldots$),
we have:

${T}_{C} = 31.666 \ldots$ degree Celsius.