Convert cun(公寸) to league
Learn how to convert
1
cun(公寸) to
league
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(cun(公寸)\right)={\color{rgb(20,165,174)} x}\left(league\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(cun(公寸)\right) = {\color{rgb(89,182,91)} 10^{-1}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-1}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(league\right) = {\color{rgb(125,164,120)} 4828.032\left(meter\right)} = {\color{rgb(125,164,120)} 4828.032\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(cun(公寸)\right)={\color{rgb(20,165,174)} x}\left(league\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-1}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4828.032}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-1}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4828.032} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-1}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4828.032} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-1} = {\color{rgb(20,165,174)} x} \times 4828.032\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4828.032 = 10^{-1}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4828.032}\right)\)
\({\color{rgb(20,165,174)} x} \times 4828.032 \times \dfrac{1.0}{4828.032} = 10^{-1} \times \dfrac{1.0}{4828.032}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4828.032}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4828.032}}} = 10^{-1} \times \dfrac{1.0}{4828.032}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-1}}{4828.032}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000207124\approx2.0712 \times 10^{-5}\)
\(\text{Conversion Equation}\)
\(1.0\left(cun(公寸)\right)\approx{\color{rgb(20,165,174)} 2.0712 \times 10^{-5}}\left(league\right)\)
