Convert grain / cubic meter to parts per million
Learn how to convert
1
grain / cubic meter to
parts per million
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(parts \text{ } per \text{ } million\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(parts \text{ } per \text{ } million\right) = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(parts \text{ } per \text{ } million\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(6.479891 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(6.479891 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(6.479891 \times 10^{-2} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 6.479891 \times 10^{-2}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.06479891\approx6.4799 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 6.4799 \times 10^{-2}}\left(parts \text{ } per \text{ } million\right)\)
