# Convert gauge to light-second

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

## Calculation Breakdown

Set up the equation
$$1.0\left(gauge\right)={\color{rgb(20,165,174)} x}\left(light-second\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(meter\right)$$
$$\text{Left side: 1.0 } \left(gauge\right) = {\color{rgb(89,182,91)} 1.435\left(meter\right)} = {\color{rgb(89,182,91)} 1.435\left(m\right)}$$
$$\text{Right side: 1.0 } \left(light-second\right) = {\color{rgb(125,164,120)} 299792458.0\left(meter\right)} = {\color{rgb(125,164,120)} 299792458.0\left(m\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(gauge\right)={\color{rgb(20,165,174)} x}\left(light-second\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1.435} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 299792458.0}} \times {\color{rgb(125,164,120)} \left(meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1.435} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 299792458.0} \cdot {\color{rgb(125,164,120)} \left(m\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1.435} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 299792458.0} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}$$
$$\text{Conversion Equation}$$
$$1.435 = {\color{rgb(20,165,174)} x} \times 299792458.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 299792458.0 = 1.435$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{299792458.0}\right)$$
$${\color{rgb(20,165,174)} x} \times 299792458.0 \times \dfrac{1.0}{299792458.0} = 1.435 \times \dfrac{1.0}{299792458.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{299792458.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{299792458.0}}} = 1.435 \times \dfrac{1.0}{299792458.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.435}{299792458.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000000048\approx4.7866 \times 10^{-9}$$
$$\text{Conversion Equation}$$
$$1.0\left(gauge\right)\approx{\color{rgb(20,165,174)} 4.7866 \times 10^{-9}}\left(light-second\right)$$