Convert cun(公寸) to hand
Learn how to convert
1
cun(公寸) to
hand
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(cun(公寸)\right)={\color{rgb(20,165,174)} x}\left(hand\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(cun(公寸)\right) = {\color{rgb(89,182,91)} 10^{-1}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-1}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(hand\right) = {\color{rgb(125,164,120)} 0.1016\left(meter\right)} = {\color{rgb(125,164,120)} 0.1016\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(cun(公寸)\right)={\color{rgb(20,165,174)} x}\left(hand\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-1}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 0.1016}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-1}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 0.1016} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-1}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 0.1016} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-1} = {\color{rgb(20,165,174)} x} \times 0.1016\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 0.1016 = 10^{-1}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{0.1016}\right)\)
\({\color{rgb(20,165,174)} x} \times 0.1016 \times \dfrac{1.0}{0.1016} = 10^{-1} \times \dfrac{1.0}{0.1016}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{0.1016}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{0.1016}}} = 10^{-1} \times \dfrac{1.0}{0.1016}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-1}}{0.1016}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.9842519685\approx9.8425 \times 10^{-1}\)
\(\text{Conversion Equation}\)
\(1.0\left(cun(公寸)\right)\approx{\color{rgb(20,165,174)} 9.8425 \times 10^{-1}}\left(hand\right)\)
