Convert astronomical unit to jo(丈)
Learn how to convert
1
astronomical unit to
jo(丈)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(astronomical \text{ } unit\right)={\color{rgb(20,165,174)} x}\left(jo(丈)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(meter\right)\)
\(\text{Left side: 1.0 } \left(astronomical \text{ } unit\right) = {\color{rgb(89,182,91)} 149597870691.0\left(meter\right)} = {\color{rgb(89,182,91)} 149597870691.0\left(m\right)}\)
\(\text{Right side: 1.0 } \left(jo(丈)\right) = {\color{rgb(125,164,120)} \dfrac{10^{2}}{33.0}\left(meter\right)} = {\color{rgb(125,164,120)} \dfrac{10^{2}}{33.0}\left(m\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(astronomical \text{ } unit\right)={\color{rgb(20,165,174)} x}\left(jo(丈)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 149597870691.0} \times {\color{rgb(89,182,91)} \left(meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{2}}{33.0}}} \times {\color{rgb(125,164,120)} \left(meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 149597870691.0} \cdot {\color{rgb(89,182,91)} \left(m\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{2}}{33.0}} \cdot {\color{rgb(125,164,120)} \left(m\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 149597870691.0} \cdot {\color{rgb(89,182,91)} \cancel{\left(m\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{2}}{33.0}} \times {\color{rgb(125,164,120)} \cancel{\left(m\right)}}\)
\(\text{Conversion Equation}\)
\(149597870691.0 = {\color{rgb(20,165,174)} x} \times \dfrac{10^{2}}{33.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{2}}{33.0} = 149597870691.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{33.0}{10^{2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{2}}{33.0} \times \dfrac{33.0}{10^{2}} = 149597870691.0 \times \dfrac{33.0}{10^{2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{2}}} \times {\color{rgb(99,194,222)} \cancel{33.0}}}{{\color{rgb(99,194,222)} \cancel{33.0}} \times {\color{rgb(255,204,153)} \cancel{10^{2}}}} = 149597870691.0 \times \dfrac{33.0}{10^{2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{149597870691.0 \times 33.0}{10^{2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{-2} \times 149597870691.0 \times 33.0\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 49367297328\approx4.9367 \times 10^{10}\)
\(\text{Conversion Equation}\)
\(1.0\left(astronomical \text{ } unit\right)\approx{\color{rgb(20,165,174)} 4.9367 \times 10^{10}}\left(jo(丈)\right)\)
