Convert foot to light-year
Learn how to convert
1
foot to
light-year
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(foot\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(foot\right) = {\color{rgb(89,182,91)} 0.3048\left(meter\right)} = {\color{rgb(89,182,91)} 0.3048\left(m\right)}\)
\(\text{Right side: 1.0 } \left(light-year\right) = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(meter\right)} = {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(foot\right)={\color{rgb(20,165,174)} x}\left(light-year\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 0.3048} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 0.3048} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 0.3048} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 9.4607304725808 \times 10^{15}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(0.3048 = {\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15} = 0.3048\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{9.4607304725808 \times 10^{15}}\right)\)
\({\color{rgb(20,165,174)} x} \times 9.4607304725808 \times 10^{15} \times \dfrac{1.0}{9.4607304725808 \times 10^{15}} = 0.3048 \times \dfrac{1.0}{9.4607304725808 \times 10^{15}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{15}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{9.4607304725808}} \times {\color{rgb(99,194,222)} \cancel{10^{15}}}} = 0.3048 \times \dfrac{1.0}{9.4607304725808 \times 10^{15}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.3048}{9.4607304725808 \times 10^{15}}\)
Rewrite equation
\(\dfrac{1.0}{10^{15}}\text{ can be rewritten to }10^{-15}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-15} \times 0.3048}{9.4607304725808}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3.2217385421 \times 10^{-17}\approx3.2217 \times 10^{-17}\)
\(\text{Conversion Equation}\)
\(1.0\left(foot\right)\approx{\color{rgb(20,165,174)} 3.2217 \times 10^{-17}}\left(light-year\right)\)
