Convert ge(合) to dan(市石)

Learn how to convert 1 ge(合) to dan(市石) step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(ge(合)\right)={\color{rgb(20,165,174)} x}\left(dan(市石)\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)

\(\text{Left side: 1.0 } \left(ge(合)\right) = {\color{rgb(89,182,91)} 10^{-4}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 10^{-4}\left(m^{3}\right)}\)

\(\text{Right side: 1.0 } \left(dan(市石)\right) = {\color{rgb(125,164,120)} 10^{-1}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 10^{-1}\left(m^{3}\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(ge(合)\right)={\color{rgb(20,165,174)} x}\left(dan(市石)\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-1}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-1}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-1}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)

\(\text{Conversion Equation}\)

\(10^{-4} = {\color{rgb(20,165,174)} x} \times 10^{-1}\)

Cancel factors on both sides

\(\text{Cancel factors}\)

\({\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-4}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}\)

\(\text{Simplify}\)

\(10^{-3} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = 10^{-3}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x} = 10^{-3}\)

\(\text{Conversion Equation}\)