# How do you convert 0.320 atm to mm Hg?

Jul 23, 2016

$P = 243.2$ $m m$ $H g$

#### Explanation:

Remember that $1$ $a t m$ $= 760$ $m m$ $H g$, from there you have 3 methods you could use:

1) Use the "rule of three"

I'm not quite sure how you call that in English, but the concept is simple

$1$ $a t m \to 760$ $m m$ $H g$
$0.320$ $a t m \to x$ $m m$ $H g$

From there, multiply in a "cross fashion", i.e.:

$1$ $a t m$ $\cdot$ $x$ $m m$ $H g$ $= 760$ $m m$ $H g$ $\cdot 0.320$ $a t m$
$x$ $m m$ $H g$ $= 243.2$ $m m$ $H g$
$x = 243.2$

2) Use a conversion factor

Since $1$ $a t m$ $= 760$ $m m$ $H g$ is an equality, it means that $\frac{1 a t m}{760 m m H g}$ and $\frac{760 m m H g}{1 a t m}$ equals 1, and as such, we can just multiply it by our valor and without changing it.

$0.320 a t m \cdot \frac{760 m m H g}{1 a t m} = 243.2 \frac{m m H g \cdot a t m}{a t m} = 243.2 m m H g$

3) Use the conversion formula of linear scales

The conversion formula of all linear scales say "the ratio of the distance between your value and a set value and the distance between two set points is always the same regardless of scale", or, in simpler terms,

$\frac{{P}_{a} - {P}_{a t m}}{{P}_{a t m} - {P}_{v a c}} = \frac{{P}_{H} - {P}_{H g a t m}}{{P}_{H g a t m} - {P}_{H g v a c}}$

Where ${P}_{a}$ is the pressure is $a t m$ and ${P}_{H}$ is the pressure in $m m H g$, throwing all values into the formula we have

$\frac{0.320 - 1}{1 - 0} = \frac{{P}_{H} - 760}{760 - 0}$
$- 0.680 \cdot 760 = {P}_{H} - 760$
$- 516.8 = {P}_{H} - 760$
${P}_{H} = 243.2$