Convert line to li(厘)

Learn how to convert 1 line to li(厘) step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(line\right)={\color{rgb(20,165,174)} x}\left(li(厘)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(line\right) = {\color{rgb(89,182,91)} \dfrac{2.11455}{999.0}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{2.11455}{999.0}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(li(厘)\right) = {\color{rgb(125,164,120)} 10^{-3}\left(meter\right)} = {\color{rgb(125,164,120)} 10^{-3}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(line\right)={\color{rgb(20,165,174)} x}\left(li(厘)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.11455}{999.0}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-3}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.11455}{999.0}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.11455}{999.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.11455}{999.0} = {\color{rgb(20,165,174)} x} \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{-3} = \dfrac{2.11455}{999.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{-3} \times \dfrac{1.0}{10^{-3}} = \dfrac{2.11455}{999.0} \times \dfrac{1.0}{10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-3}}}} = \dfrac{2.11455 \times 1.0}{999.0 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.11455}{999.0 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 2.11455}{999.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx2.1166666667\approx2.1167\)
\(\text{Conversion Equation}\)
\(1.0\left(line\right)\approx{\color{rgb(20,165,174)} 2.1167}\left(li(厘)\right)\)

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