Convert ounce / cubic meter to pound / fluid-ounce
Learn how to convert
1
ounce / cubic meter to
pound / fluid-ounce
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ounce}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{fluid-ounce}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ounce}{cubic \text{ } meter}\right) = {\color{rgb(89,182,91)} 2.8349523125 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 2.8349523125 \times 10^{-2}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{fluid-ounce}\right) = {\color{rgb(125,164,120)} \dfrac{5.0}{2.95735295625 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{5.0}{2.95735295625 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ounce}{cubic \text{ } meter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{fluid-ounce}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.8349523125 \times 10^{-2}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{5.0}{2.95735295625 \times 10^{-4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.8349523125 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{5.0}{2.95735295625 \times 10^{-4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.8349523125 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{5.0}{2.95735295625 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(2.8349523125 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{2.95735295625 \times 10^{-4}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{2.95735295625 \times 10^{-4}} = 2.8349523125 \times 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{2.95735295625 \times 10^{-4}}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{2.95735295625 \times 10^{-4}} \times \dfrac{2.95735295625 \times 10^{-4}}{5.0} = 2.8349523125 \times 10^{-2} \times \dfrac{2.95735295625 \times 10^{-4}}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{5.0}} \times {\color{rgb(99,194,222)} \cancel{2.95735295625}} \times {\color{rgb(166,218,227)} \cancel{10^{-4}}}}{{\color{rgb(99,194,222)} \cancel{2.95735295625}} \times {\color{rgb(166,218,227)} \cancel{10^{-4}}} \times {\color{rgb(255,204,153)} \cancel{5.0}}} = 2.8349523125 \times 10^{-2} \times \dfrac{2.95735295625 \times 10^{-4}}{5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.8349523125 \times 10^{-2} \times 2.95735295625 \times 10^{-4}}{5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000016768\approx1.6768 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ounce}{cubic \text{ } meter}\right)\approx{\color{rgb(20,165,174)} 1.6768 \times 10^{-6}}\left(\dfrac{pound}{fluid-ounce}\right)\)
