# Convert ångström to mile

Learn how to convert 1 ångström to mile step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(ångström\right)={\color{rgb(20,165,174)} x}\left(mile\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(ångström\right) = {\color{rgb(89,182,91)} 10^{-10}\left(meter\right)} = {\color{rgb(89,182,91)} 10^{-10}\left(m\right)}$$
$$\text{Right side: 1.0 } \left(mile\right) = {\color{rgb(125,164,120)} 1609.344\left(meter\right)} = {\color{rgb(125,164,120)} 1609.344\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(ångström\right)={\color{rgb(20,165,174)} x}\left(mile\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-10}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1609.344}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10^{-10}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1609.344} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-10}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1609.344} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$10^{-10} = {\color{rgb(20,165,174)} x} \times 1609.344$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 1609.344 = 10^{-10}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{1609.344}\right)$$
$${\color{rgb(20,165,174)} x} \times 1609.344 \times \dfrac{1.0}{1609.344} = 10^{-10} \times \dfrac{1.0}{1609.344}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1609.344}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1609.344}}} = 10^{-10} \times \dfrac{1.0}{1609.344}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-10}}{1609.344}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx6.2137119224 \times 10^{-14}\approx6.2137 \times 10^{-14}$$
$$\text{Conversion Equation}$$
$$1.0\left(ångström\right)\approx{\color{rgb(20,165,174)} 6.2137 \times 10^{-14}}\left(mile\right)$$