Convert square chain to go(合)
Learn how to convert
1
square chain to
go(合)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(square \text{ } chain\right)={\color{rgb(20,165,174)} x}\left(go(合)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(square \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(square \text{ } chain\right) = {\color{rgb(89,182,91)} 4.0 \times 10^{2}\left(square \text{ } meter\right)} = {\color{rgb(89,182,91)} 4.0 \times 10^{2}\left(m^{2}\right)}\)
\(\text{Right side: 1.0 } \left(go(合)\right) = {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{2}}{121.0}\left(square \text{ } meter\right)} = {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{2}}{121.0}\left(m^{2}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(square \text{ } chain\right)={\color{rgb(20,165,174)} x}\left(go(合)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \times {\color{rgb(89,182,91)} \left(square \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{2}}{121.0}}} \times {\color{rgb(125,164,120)} \left(square \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \left(m^{2}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{2}}{121.0}} \cdot {\color{rgb(125,164,120)} \left(m^{2}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{2}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{2}}{121.0}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{2}\right)}}\)
\(\text{Conversion Equation}\)
\(4.0 \times 10^{2} = {\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times 10^{2}}{121.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(4.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}}}{121.0}\)
\(\text{Simplify}\)
\(4.0 = {\color{rgb(20,165,174)} x} \times \dfrac{2.0}{121.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.0}{121.0} = 4.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{121.0}{2.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.0}{121.0} \times \dfrac{121.0}{2.0} = 4.0 \times \dfrac{121.0}{2.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.0}} \times {\color{rgb(99,194,222)} \cancel{121.0}}}{{\color{rgb(99,194,222)} \cancel{121.0}} \times {\color{rgb(255,204,153)} \cancel{2.0}}} = 4.0 \times \dfrac{121.0}{2.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.0 \times 121.0}{2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 242 = 2.42 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(square \text{ } chain\right) = {\color{rgb(20,165,174)} 2.42 \times 10^{2}}\left(go(合)\right)\)
