Convert fen(市分) to light-year

Learn how to convert 1 fen(市分) to light-year step by step.

Calculation Breakdown

Set up the equation

\(1.0\left(fen(市分)\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)

\(\text{Left side: 1.0 } \left(fen(市分)\right) = {\color{rgb(89,182,91)} \dfrac{1.0}{3.0 \times 10^{2}}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{1.0}{3.0 \times 10^{2}}\left(m\right)}\)

\(\text{Right side: 1.0 } \left(light-year\right) = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(meter\right)} = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(m\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(fen(市分)\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.0 \times 10^{2}}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1.0}{3.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1.0}{3.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{1.0}{3.0 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15}\)

Switch sides

\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15} = \dfrac{1.0}{3.0 \times 10^{2}}\)

Isolate \({\color{rgb(20,165,174)} x}\)

Multiply both sides by \(\left(\dfrac{1.0}{9.4607304725808 \times 10^{15}}\right)\)

\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15} \times \dfrac{1.0}{9.4607304725808 \times 10^{15}} = \dfrac{1.0}{3.0 \times 10^{2}} \times \dfrac{1.0}{9.4607304725808 \times 10^{15}}\)

\(\text{Cancel}\)

\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{15}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{15}}}} = \dfrac{1.0 \times 1.0}{3.0 \times 10^{2} \times 9.4607304725808 \times 10^{15}}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{3.0 \times 10^{2} \times 9.4607304725808 \times 10^{15}}\)

Rewrite equation

\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)

\(\dfrac{1.0}{10^{15}}\text{ can be rewritten to }10^{-15}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 10^{-15}}{3.0 \times 9.4607304725808}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = \dfrac{10^{-17}}{3.0 \times 9.4607304725808}\)

Solve \({\color{rgb(20,165,174)} x}\)

\({\color{rgb(20,165,174)} x}\approx3.5233361134 \times 10^{-19}\approx3.5233 \times 10^{-19}\)

\(\text{Conversion Equation}\)