Convert parts per million to grain / liter
Learn how to convert
1
parts per million to
grain / liter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(parts \text{ } per \text{ } million\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{liter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(parts \text{ } per \text{ } million\right) = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{grain}{liter}\right) = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(parts \text{ } per \text{ } million\right)={\color{rgb(20,165,174)} x}\left(\dfrac{grain}{liter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-3} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}}}{10^{-3}}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}}{{\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-3}}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{6.479891}{10^{-1}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891}{10^{-1}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{10^{-1}}{6.479891}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{6.479891}{10^{-1}} \times \dfrac{10^{-1}}{6.479891} = \times \dfrac{10^{-1}}{6.479891}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{6.479891}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}}{{\color{rgb(99,194,222)} \cancel{10^{-1}}} \times {\color{rgb(255,204,153)} \cancel{6.479891}}} = \dfrac{10^{-1}}{6.479891}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-1}}{6.479891}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0154323584\approx1.5432 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(parts \text{ } per \text{ } million\right)\approx{\color{rgb(20,165,174)} 1.5432 \times 10^{-2}}\left(\dfrac{grain}{liter}\right)\)
