Convert ligne to parsec
Learn how to convert
1
ligne to
parsec
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(ligne\right)={\color{rgb(20,165,174)} x}\left(parsec\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(ligne\right) = {\color{rgb(89,182,91)} \dfrac{0.2233275}{99.0}\left(meter\right)} = {\color{rgb(89,182,91)} \dfrac{0.2233275}{99.0}\left(m\right)}\)
\(\text{Right side: 1.0 } \left(parsec\right) = {\color{rgb(125,164,120)} 3.08567400801506 \times 10^{16}\left(meter\right)} = {\color{rgb(125,164,120)} 3.08567400801506 \times 10^{16}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(ligne\right)={\color{rgb(20,165,174)} x}\left(parsec\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.2233275}{99.0}} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.08567400801506 \times 10^{16}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.2233275}{99.0}} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.08567400801506 \times 10^{16}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.2233275}{99.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.08567400801506 \times 10^{16}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{0.2233275}{99.0} = {\color{rgb(20,165,174)} x} \times 3.08567400801506 \times 10^{16}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 3.08567400801506 \times 10^{16} = \dfrac{0.2233275}{99.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{3.08567400801506 \times 10^{16}}\right)\)
\({\color{rgb(20,165,174)} x} \times 3.08567400801506 \times 10^{16} \times \dfrac{1.0}{3.08567400801506 \times 10^{16}} = \dfrac{0.2233275}{99.0} \times \dfrac{1.0}{3.08567400801506 \times 10^{16}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.08567400801506}} \times {\color{rgb(99,194,222)} \cancel{10^{16}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.08567400801506}} \times {\color{rgb(99,194,222)} \cancel{10^{16}}}} = \dfrac{0.2233275 \times 1.0}{99.0 \times 3.08567400801506 \times 10^{16}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.2233275}{99.0 \times 3.08567400801506 \times 10^{16}}\)
Rewrite equation
\(\dfrac{1.0}{10^{16}}\text{ can be rewritten to }10^{-16}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-16} \times 0.2233275}{99.0 \times 3.08567400801506}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx7.3106664135 \times 10^{-20}\approx7.3107 \times 10^{-20}\)
\(\text{Conversion Equation}\)
\(1.0\left(ligne\right)\approx{\color{rgb(20,165,174)} 7.3107 \times 10^{-20}}\left(parsec\right)\)
