# Convert light-second to mile

Learn how to convert 1 light-second to mile step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(light-second\right)={\color{rgb(20,165,174)} x}\left(mile\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(light-second\right) = {\color{rgb(89,182,91)} 299792458.0\left(meter\right)} = {\color{rgb(89,182,91)} 299792458.0\left(m\right)}$$
$$\text{Right side: 1.0 } \left(mile\right) = {\color{rgb(125,164,120)} 1853.184\left(meter\right)} = {\color{rgb(125,164,120)} 1853.184\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(light-second\right)={\color{rgb(20,165,174)} x}\left(mile\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 299792458.0} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1853.184}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 299792458.0} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1853.184} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 299792458.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1853.184} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$299792458.0 = {\color{rgb(20,165,174)} x} \times 1853.184$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 1853.184 = 299792458.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{1853.184}\right)$$
$${\color{rgb(20,165,174)} x} \times 1853.184 \times \dfrac{1.0}{1853.184} = 299792458.0 \times \dfrac{1.0}{1853.184}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1853.184}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1853.184}}} = 299792458.0 \times \dfrac{1.0}{1853.184}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{299792458.0}{1853.184}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx161771.55533\approx1.6177 \times 10^{5}$$
$$\text{Conversion Equation}$$
$$1.0\left(light-second\right)\approx{\color{rgb(20,165,174)} 1.6177 \times 10^{5}}\left(mile\right)$$