Convert li(里) to light-year
Learn how to convert
1
li(里) to
light-year
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(li(里)\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(li(里)\right) = {\color{rgb(89,182,91)} 5.0 \times 10^{2}\left(meter\right)} = {\color{rgb(89,182,91)} 5.0 \times 10^{2}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(light-year\right) = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(meter\right)} = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(li(里)\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(5.0 \times 10^{2} = {\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(5.0 \times {\color{rgb(255,204,153)} \cancel{10^{2}}} = {\color{rgb(20,165,174)} x} \times 9.4607304725808 \times {\color{rgb(255,204,153)} \cancelto{10^{13}}{10^{15}}}\)
\(\text{Simplify}\)
\(5.0 = {\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{13}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{13} = 5.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{9.4607304725808 \times 10^{13}}\right)\)
\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{13} \times \dfrac{1.0}{9.4607304725808 \times 10^{13}} = 5.0 \times \dfrac{1.0}{9.4607304725808 \times 10^{13}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{13}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{13}}}} = 5.0 \times \dfrac{1.0}{9.4607304725808 \times 10^{13}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{5.0}{9.4607304725808 \times 10^{13}}\)
Rewrite equation
\(\dfrac{1.0}{10^{13}}\text{ can be rewritten to }10^{-13}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-13} \times 5.0}{9.4607304725808}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx5.2850041701 \times 10^{-14}\approx5.285 \times 10^{-14}\)
\(\text{Conversion Equation}\)
\(1.0\left(li(里)\right)\approx{\color{rgb(20,165,174)} 5.285 \times 10^{-14}}\left(light-year\right)\)
