Convert light-second to hao(毫)
Learn how to convert
1
light-second to
hao(毫)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(light-second\right)={\color{rgb(20,165,174)} x}\left(hao(毫)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(light-second\right) = {\color{rgb(89,182,91)} 299792458.0\left(meter\right)} = {\color{rgb(89,182,91)} 299792458.0\left(m\right)}\)
\(\text{Right side: 1.0 } \left(hao(毫)\right) = {\color{rgb(125,164,120)} \dfrac{1.0}{3.0 \times 10^{4}}\left(meter\right)} = {\color{rgb(125,164,120)} \dfrac{1.0}{3.0 \times 10^{4}}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(light-second\right)={\color{rgb(20,165,174)} x}\left(hao(毫)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 299792458.0} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1.0}{3.0 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 299792458.0} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1.0}{3.0 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 299792458.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1.0}{3.0 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(299792458.0 = {\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.0 \times 10^{4}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.0 \times 10^{4}} = 299792458.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.0 \times 10^{4}}{1.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1.0}{3.0 \times 10^{4}} \times \dfrac{3.0 \times 10^{4}}{1.0} = 299792458.0 \times \dfrac{3.0 \times 10^{4}}{1.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{3.0}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}}}{{\color{rgb(99,194,222)} \cancel{3.0}} \times {\color{rgb(166,218,227)} \cancel{10^{4}}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = 299792458.0 \times \dfrac{3.0 \times 10^{4}}{1.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = 299792458.0 \times 3.0 \times 10^{4}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 8.99377374 \times 10^{12}\approx8.9938 \times 10^{12}\)
\(\text{Conversion Equation}\)
\(1.0\left(light-second\right)\approx{\color{rgb(20,165,174)} 8.9938 \times 10^{12}}\left(hao(毫)\right)\)
