Convert pound / liter to ton / bushel
Learn how to convert
1
pound / liter to
ton / bushel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ton}{bushel}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{liter}\right) = {\color{rgb(89,182,91)} 5.0 \times 10^{2}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} 5.0 \times 10^{2}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{ton}{bushel}\right) = {\color{rgb(125,164,120)} \dfrac{10^{5}}{3.636872}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{10^{5}}{3.636872}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{ton}{bushel}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{5}}{3.636872}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{5}}{3.636872}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{5}}{3.636872}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(5.0 \times 10^{2} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{5}}{3.636872}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(5.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancelto{10^{3}}{10^{5}}}}{3.636872}\)
\(\text{Simplify}\)
\(5.0 = {\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{3.636872}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{3.636872} = 5.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.636872}{10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{3}}{3.636872} \times \dfrac{3.636872}{10^{3}} = 5.0 \times \dfrac{3.636872}{10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{3}}} \times {\color{rgb(99,194,222)} \cancel{3.636872}}}{{\color{rgb(99,194,222)} \cancel{3.636872}} \times {\color{rgb(255,204,153)} \cancel{10^{3}}}} = 5.0 \times \dfrac{3.636872}{10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{5.0 \times 3.636872}{10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{-3} \times 5.0 \times 3.636872\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.01818436\approx1.8184 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{liter}\right)\approx{\color{rgb(20,165,174)} 1.8184 \times 10^{-2}}\left(\dfrac{ton}{bushel}\right)\)
