Convert light-year to li(里)
Learn how to convert
1
light-year to
li(里)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(light-year\right)={\color{rgb(20,165,174)} x}\left(li(里)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(light-year\right) = {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}\left(meter\right)} = {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(li(里)\right) = {\color{rgb(125,164,120)} 5.0 \times 10^{2}\left(meter\right)} = {\color{rgb(125,164,120)} 5.0 \times 10^{2}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(light-year\right)={\color{rgb(20,165,174)} x}\left(li(里)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 5.0 \times 10^{2}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 5.0 \times 10^{2}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 5.0 \times 10^{2}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(9.4607304725808 \times 10^{15} = {\color{rgb(20,165,174)} x} \times 5.0 \times 10^{2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(9.4607304725808 \times {\color{rgb(255,204,153)} \cancelto{10^{13}}{10^{15}}} = {\color{rgb(20,165,174)} x} \times 5.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}}\)
\(\text{Simplify}\)
\(9.4607304725808 \times 10^{13} = {\color{rgb(20,165,174)} x} \times 5.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 5.0 = 9.4607304725808 \times 10^{13}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 5.0 \times \dfrac{1.0}{5.0} = 9.4607304725808 \times 10^{13} \times \dfrac{1.0}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{5.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{5.0}}} = 9.4607304725808 \times 10^{13} \times \dfrac{1.0}{5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{9.4607304725808 \times 10^{13}}{5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1.8921460945 \times 10^{13}\approx1.8921 \times 10^{13}\)
\(\text{Conversion Equation}\)
\(1.0\left(light-year\right)\approx{\color{rgb(20,165,174)} 1.8921 \times 10^{13}}\left(li(里)\right)\)
