Convert yin(引) to cho(町)
Learn how to convert
1
yin(引) to
cho(町)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(yin(引)\right)={\color{rgb(20,165,174)} x}\left(cho(町)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(yin(引)\right) = {\color{rgb(89,182,91)} \dfrac{10^{2}}{3.0}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{10^{2}}{3.0}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(cho(町)\right) = {\color{rgb(125,164,120)} \dfrac{1.2 \times 10^{3}}{11.0}\left(meter\right)} = {\color{rgb(125,164,120)} \dfrac{1.2 \times 10^{3}}{11.0}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(yin(引)\right)={\color{rgb(20,165,174)} x}\left(cho(町)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{2}}{3.0}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.2 \times 10^{3}}{11.0}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{2}}{3.0}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.2 \times 10^{3}}{11.0}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{2}}{3.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.2 \times 10^{3}}{11.0}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{2}}{3.0} = {\color{rgb(20,165,174)} x} \times \dfrac{1.2 \times 10^{3}}{11.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancel{10^{2}}}}{3.0} = {\color{rgb(20,165,174)} x} \times \dfrac{1.2 \times {\color{rgb(255,204,153)} \cancelto{10}{10^{3}}}}{11.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.2 \times 10.0}{11.0} = \dfrac{1.0}{3.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{11.0}{1.2 \times 10.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.2 \times 10.0}{11.0} \times \dfrac{11.0}{1.2 \times 10.0} = \dfrac{1.0}{3.0} \times \dfrac{11.0}{1.2 \times 10.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.2}} \times {\color{rgb(99,194,222)} \cancel{10.0}} \times {\color{rgb(166,218,227)} \cancel{11.0}}}{{\color{rgb(166,218,227)} \cancel{11.0}} \times {\color{rgb(255,204,153)} \cancel{1.2}} \times {\color{rgb(99,194,222)} \cancel{10.0}}} = \dfrac{1.0 \times 11.0}{3.0 \times 1.2 \times 10.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{11.0}{3.0 \times 1.2 \times 10.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.3055555556\approx3.0556 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(yin(引)\right)\approx{\color{rgb(20,165,174)} 3.0556 \times 10^{-1}}\left(cho(町)\right)\)
