Convert ligne to light-second
Learn how to convert
1
ligne to
light-second
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(ligne\right)={\color{rgb(20,165,174)} x}\left(light-second\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(ligne\right) = {\color{rgb(89,182,91)} 2.256 \times 10^{-3}\left(meter\right)} = {\color{rgb(89,182,91)} 2.256 \times 10^{-3}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(light-second\right) = {\color{rgb(125,164,120)} 299792458.0\left(meter\right)} = {\color{rgb(125,164,120)} 299792458.0\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(ligne\right)={\color{rgb(20,165,174)} x}\left(light-second\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.256 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 299792458.0}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.256 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 299792458.0} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.256 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 299792458.0} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(2.256 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 299792458.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 299792458.0 = 2.256 \times 10^{-3}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{299792458.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 299792458.0 \times \dfrac{1.0}{299792458.0} = 2.256 \times 10^{-3} \times \dfrac{1.0}{299792458.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{299792458.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{299792458.0}}} = 2.256 \times 10^{-3} \times \dfrac{1.0}{299792458.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.256 \times 10^{-3}}{299792458.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx7.5252059877 \times 10^{-12}\approx7.5252 \times 10^{-12}\)
\(\text{Conversion Equation}\)
\(1.0\left(ligne\right)\approx{\color{rgb(20,165,174)} 7.5252 \times 10^{-12}}\left(light-second\right)\)
