Convert grain / cubic meter to parts per billion
Learn how to convert
1
grain / cubic meter to
parts per billion
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(parts \text{ } per \text{ } billion\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{grain}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(parts \text{ } per \text{ } billion\right) = {\color{rgb(125,164,120)} 10^{-6}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 10^{-6}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(parts \text{ } per \text{ } billion\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-6}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-6}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-6}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(6.479891 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times 10^{-6}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(6.479891 \times {\color{rgb(255,204,153)} \cancel{10^{-5}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-6}}}\)
\(\text{Simplify}\)
\(6.479891 = {\color{rgb(20,165,174)} x} \times 10^{-1}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-1} = 6.479891\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-1} \times \dfrac{1.0}{10^{-1}} = 6.479891 \times \dfrac{1.0}{10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-1}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-1}}}} = 6.479891 \times \dfrac{1.0}{10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.479891}{10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10.0 \times 6.479891\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 64.79891\approx64.7989\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{grain}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 64.7989}\left(parts \text{ } per \text{ } billion\right)\)
