Convert cun(寸) to gauge

Learn how to convert 1 cun(寸) to gauge step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(cun(寸)\right)={\color{rgb(20,165,174)} x}\left(gauge\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(cun(寸)\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{30.0}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{30.0}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(gauge\right) = {\color{rgb(125,164,120)} 1.435\left(meter\right)} = {\color{rgb(125,164,120)} 1.435\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(cun(寸)\right)={\color{rgb(20,165,174)} x}\left(gauge\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{30.0}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.435}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{30.0}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.435} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{30.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.435} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1.0}{30.0} = {\color{rgb(20,165,174)} x} \times 1.435\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.435 = \dfrac{1.0}{30.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.435}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.435 \times \dfrac{1.0}{1.435} = \dfrac{1.0}{30.0} \times \dfrac{1.0}{1.435}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.435}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.435}}} = \dfrac{1.0 \times 1.0}{30.0 \times 1.435}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{30.0 \times 1.435}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0232288037\approx2.3229 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(cun(寸)\right)\approx{\color{rgb(20,165,174)} 2.3229 \times 10^{-2}}\left(gauge\right)\)

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