Convert ge(合) to sho(升)
Learn how to convert
1
ge(合) to
sho(升)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(ge(合)\right)={\color{rgb(20,165,174)} x}\left(sho(升)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(ge(合)\right) = {\color{rgb(89,182,91)} 10^{-4}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 10^{-4}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(sho(升)\right) = {\color{rgb(125,164,120)} \dfrac{2.401}{1.331 \times 10^{3}}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} \dfrac{2.401}{1.331 \times 10^{3}}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(ge(合)\right)={\color{rgb(20,165,174)} x}\left(sho(升)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.401}{1.331 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.401}{1.331 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.401}{1.331 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-4} = {\color{rgb(20,165,174)} x} \times \dfrac{2.401}{1.331 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.401}{1.331 \times 10^{3}} = 10^{-4}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.331 \times 10^{3}}{2.401}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.401}{1.331 \times 10^{3}} \times \dfrac{1.331 \times 10^{3}}{2.401} = 10^{-4} \times \dfrac{1.331 \times 10^{3}}{2.401}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.401}} \times {\color{rgb(99,194,222)} \cancel{1.331}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{1.331}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{2.401}}} = {\color{rgb(255,204,153)} \cancelto{10^{-1}}{10^{-4}}} \times \dfrac{1.331 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}{2.401}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-1} \times 1.331}{2.401}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0554352353\approx5.5435 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(ge(合)\right)\approx{\color{rgb(20,165,174)} 5.5435 \times 10^{-2}}\left(sho(升)\right)\)
