Convert juchart to qing(顷)
Learn how to convert
1
juchart to
qing(顷)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(juchart\right)={\color{rgb(20,165,174)} x}\left(qing(顷)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(square \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(juchart\right) = {\color{rgb(89,182,91)} 4.5 \times 10^{3}\left(square \text{ } meter\right)} = {\color{rgb(89,182,91)} 4.5 \times 10^{3}\left(m^{2}\right)}\)
\(\text{Right side: 1.0 } \left(qing(顷)\right) = {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{5}}{3.0}\left(square \text{ } meter\right)} = {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{5}}{3.0}\left(m^{2}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(juchart\right)={\color{rgb(20,165,174)} x}\left(qing(顷)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 4.5 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(square \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{5}}{3.0}}} \times {\color{rgb(125,164,120)} \left(square \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 4.5 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(m^{2}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{5}}{3.0}} \cdot {\color{rgb(125,164,120)} \left(m^{2}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 4.5 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{2}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.0 \times 10^{5}}{3.0}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{2}\right)}}\)
\(\text{Conversion Equation}\)
\(4.5 \times 10^{3} = {\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times 10^{5}}{3.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(4.5 \times {\color{rgb(255,204,153)} \cancel{10^{3}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}}{3.0}\)
\(\text{Simplify}\)
\(4.5 = {\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times 10^{2}}{3.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times 10^{2}}{3.0} = 4.5\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.0}{2.0 \times 10^{2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.0 \times 10^{2}}{3.0} \times \dfrac{3.0}{2.0 \times 10^{2}} = 4.5 \times \dfrac{3.0}{2.0 \times 10^{2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.0}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}} \times {\color{rgb(166,218,227)} \cancel{3.0}}}{{\color{rgb(166,218,227)} \cancel{3.0}} \times {\color{rgb(255,204,153)} \cancel{2.0}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}}} = 4.5 \times \dfrac{3.0}{2.0 \times 10^{2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.5 \times 3.0}{2.0 \times 10^{2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 4.5 \times 3.0}{2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.0675 = 6.75 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(juchart\right) = {\color{rgb(20,165,174)} 6.75 \times 10^{-2}}\left(qing(顷)\right)\)
