Convert si(丝) to cun(公寸)

Learn how to convert 1 si(丝) to cun(公寸) step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(si(丝)\right)={\color{rgb(20,165,174)} x}\left(cun(公寸)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(si(丝)\right) = {\color{rgb(89,182,91)} 10^{-5}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-5}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(cun(公寸)\right) = {\color{rgb(125,164,120)} 10^{-1}\left(meter\right)} = {\color{rgb(125,164,120)} 10^{-1}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(si(丝)\right)={\color{rgb(20,165,174)} x}\left(cun(公寸)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-1}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-1}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-1}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-5} = {\color{rgb(20,165,174)} x} \times 10^{-1}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancelto{10^{-4}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-1}}}\)
\(\text{Simplify}\)
\(10^{-4} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 10^{-4}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 10^{-4}\)
\(\text{Conversion Equation}\)
\(1.0\left(si(丝)\right) = {\color{rgb(20,165,174)} 10^{-4}}\left(cun(公寸)\right)\)

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