# Convert lap to ri(里)

Learn how to convert 1 lap to ri(里) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(lap\right)={\color{rgb(20,165,174)} x}\left(ri(里)\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(lap\right) = {\color{rgb(89,182,91)} 4.0 \times 10^{2}\left(meter\right)} = {\color{rgb(89,182,91)} 4.0 \times 10^{2}\left(m\right)}$$
$$\text{Right side: 1.0 } \left(ri(里)\right) = {\color{rgb(125,164,120)} \dfrac{4.32 \times 10^{4}}{11.0}\left(meter\right)} = {\color{rgb(125,164,120)} \dfrac{4.32 \times 10^{4}}{11.0}\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(lap\right)={\color{rgb(20,165,174)} x}\left(ri(里)\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{4.32 \times 10^{4}}{11.0}}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{4.32 \times 10^{4}}{11.0}} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 4.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{4.32 \times 10^{4}}{11.0}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$4.0 \times 10^{2} = {\color{rgb(20,165,174)} x} \times \dfrac{4.32 \times 10^{4}}{11.0}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$4.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} = {\color{rgb(20,165,174)} x} \times \dfrac{4.32 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{4}}}}{11.0}$$
$$\text{Simplify}$$
$$4.0 = {\color{rgb(20,165,174)} x} \times \dfrac{4.32 \times 10^{2}}{11.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{4.32 \times 10^{2}}{11.0} = 4.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{11.0}{4.32 \times 10^{2}}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{4.32 \times 10^{2}}{11.0} \times \dfrac{11.0}{4.32 \times 10^{2}} = 4.0 \times \dfrac{11.0}{4.32 \times 10^{2}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{4.32}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}} \times {\color{rgb(166,218,227)} \cancel{11.0}}}{{\color{rgb(166,218,227)} \cancel{11.0}} \times {\color{rgb(255,204,153)} \cancel{4.32}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}}} = 4.0 \times \dfrac{11.0}{4.32 \times 10^{2}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{4.0 \times 11.0}{4.32 \times 10^{2}}$$
Rewrite equation
$$\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 4.0 \times 11.0}{4.32}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.1018518518\approx1.0185 \times 10^{-1}$$
$$\text{Conversion Equation}$$
$$1.0\left(lap\right)\approx{\color{rgb(20,165,174)} 1.0185 \times 10^{-1}}\left(ri(里)\right)$$