Convert gram / cubic inch to pound / cubic inch
Learn how to convert
1
gram / cubic inch to
pound / cubic inch
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } inch}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{gram}{cubic \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } inch}\right) = {\color{rgb(125,164,120)} \dfrac{5.0}{1.6387064 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{5.0}{1.6387064 \times 10^{-4}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } inch}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{5.0}{1.6387064 \times 10^{-4}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{5.0}{1.6387064 \times 10^{-4}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{1.6387064 \times 10^{-2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{5.0}{1.6387064 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{1.6387064 \times 10^{-2}} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{1.6387064 \times 10^{-4}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.6387064}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{{\color{rgb(255,204,153)} \cancel{1.6387064}} \times {\color{rgb(99,194,222)} \cancelto{10^{-2}}{10^{-4}}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{10^{-2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{10^{-2}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{10^{-2}}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{10^{-2}} \times \dfrac{10^{-2}}{5.0} = \times \dfrac{10^{-2}}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{5.0}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}}{{\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(255,204,153)} \cancel{5.0}}} = \dfrac{10^{-2}}{5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2}}{5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 2 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{gram}{cubic \text{ } inch}\right) = {\color{rgb(20,165,174)} 2 \times 10^{-3}}\left(\dfrac{pound}{cubic \text{ } inch}\right)\)
