Convert parts per billion to pound / cubic meter
Learn how to convert
1
parts per billion to
pound / cubic meter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(parts \text{ } per \text{ } billion\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(parts \text{ } per \text{ } billion\right) = {\color{rgb(89,182,91)} 10^{-6}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 10^{-6}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } meter}\right) = {\color{rgb(125,164,120)} 0.45359237\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 0.45359237\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(parts \text{ } per \text{ } billion\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-6}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 0.45359237}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-6}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 0.45359237} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-6}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 0.45359237} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-6} = {\color{rgb(20,165,174)} x} \times 0.45359237\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 0.45359237 = 10^{-6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{0.45359237}\right)\)
\({\color{rgb(20,165,174)} x} \times 0.45359237 \times \dfrac{1.0}{0.45359237} = 10^{-6} \times \dfrac{1.0}{0.45359237}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{0.45359237}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{0.45359237}}} = 10^{-6} \times \dfrac{1.0}{0.45359237}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-6}}{0.45359237}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000022046\approx2.2046 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(parts \text{ } per \text{ } billion\right)\approx{\color{rgb(20,165,174)} 2.2046 \times 10^{-6}}\left(\dfrac{pound}{cubic \text{ } meter}\right)\)
