Convert pound / cubic inch to pound / liter
Learn how to convert
1
pound / cubic inch to
pound / liter
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{pound}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{liter}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{pound}{cubic \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{5.0}{1.6387064 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{5.0}{1.6387064 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{liter}\right) = {\color{rgb(125,164,120)} 5.0 \times 10^{2}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 5.0 \times 10^{2}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{liter}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{1.6387064 \times 10^{-4}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 5.0 \times 10^{2}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{5.0}{1.6387064 \times 10^{-4}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 5.0 \times 10^{2}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{5.0}{1.6387064 \times 10^{-4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 5.0 \times 10^{2}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{5.0}{1.6387064 \times 10^{-4}} = {\color{rgb(20,165,174)} x} \times 5.0 \times 10^{2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{5.0}}}{1.6387064 \times 10^{-4}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{5.0}} \times 10^{2}\)
\(\text{Simplify}\)
\(\dfrac{1.0}{1.6387064 \times 10^{-4}} = {\color{rgb(20,165,174)} x} \times 10^{2}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{2} = \dfrac{1.0}{1.6387064 \times 10^{-4}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{2}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{2} \times \dfrac{1.0}{10^{2}} = \dfrac{1.0}{1.6387064 \times 10^{-4}} \times \dfrac{1.0}{10^{2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{2}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{2}}}} = \dfrac{1.0 \times 1.0}{1.6387064 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-4}}} \times {\color{rgb(255,204,153)} \cancel{10^{2}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{1.6387064 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2}}{1.6387064}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx61.023744095\approx61.0237\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{pound}{cubic \text{ } inch}\right)\approx{\color{rgb(20,165,174)} 61.0237}\left(\dfrac{pound}{liter}\right)\)
