Convert light-year to li(公里)
Learn how to convert
1
light-year to
li(公里)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(light-year\right)={\color{rgb(20,165,174)} x}\left(li(公里)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(light-year\right) = {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}\left(meter\right)} = {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(li(公里)\right) = {\color{rgb(125,164,120)} 10^{3}\left(meter\right)} = {\color{rgb(125,164,120)} 10^{3}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(light-year\right)={\color{rgb(20,165,174)} x}\left(li(公里)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{3}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{3}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(9.4607304725808 \times 10^{15} = {\color{rgb(20,165,174)} x} \times 10^{3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(9.4607304725808 \times {\color{rgb(255,204,153)} \cancelto{10^{12}}{10^{15}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{3}}}\)
\(\text{Simplify}\)
\(9.4607304725808 \times 10^{12} = {\color{rgb(20,165,174)} x}\)
Switch sides
\({\color{rgb(20,165,174)} x} = 9.4607304725808 \times 10^{12}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx9.4607304726 \times 10^{12}\approx9.4607 \times 10^{12}\)
\(\text{Conversion Equation}\)
\(1.0\left(light-year\right)\approx{\color{rgb(20,165,174)} 9.4607 \times 10^{12}}\left(li(公里)\right)\)
