# Convert pie to ligne

Learn how to convert 1 pie to ligne step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(pie\right)={\color{rgb(20,165,174)} x}\left(ligne\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(pie\right) = {\color{rgb(89,182,91)} 0.2786\left(meter\right)} = {\color{rgb(89,182,91)} 0.2786\left(m\right)}$$
$$\text{Right side: 1.0 } \left(ligne\right) = {\color{rgb(125,164,120)} 2.256 \times 10^{-3}\left(meter\right)} = {\color{rgb(125,164,120)} 2.256 \times 10^{-3}\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(pie\right)={\color{rgb(20,165,174)} x}\left(ligne\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 0.2786} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.256 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 0.2786} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.256 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 0.2786} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.256 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$0.2786 = {\color{rgb(20,165,174)} x} \times 2.256 \times 10^{-3}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2.256 \times 10^{-3} = 0.2786$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2.256 \times 10^{-3}}\right)$$
$${\color{rgb(20,165,174)} x} \times 2.256 \times 10^{-3} \times \dfrac{1.0}{2.256 \times 10^{-3}} = 0.2786 \times \dfrac{1.0}{2.256 \times 10^{-3}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.256}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.256}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = 0.2786 \times \dfrac{1.0}{2.256 \times 10^{-3}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{0.2786}{2.256 \times 10^{-3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 0.2786}{2.256}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx123.4929078\approx1.2349 \times 10^{2}$$
$$\text{Conversion Equation}$$
$$1.0\left(pie\right)\approx{\color{rgb(20,165,174)} 1.2349 \times 10^{2}}\left(ligne\right)$$