Convert dou(市斗) to pony
Learn how to convert
1
dou(市斗) to
pony
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(dou(市斗)\right)={\color{rgb(20,165,174)} x}\left(pony\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(dou(市斗)\right) = {\color{rgb(89,182,91)} 10^{-2}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 10^{-2}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(pony\right) = {\color{rgb(125,164,120)} 2.2180147171875 \times 10^{-5}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 2.2180147171875 \times 10^{-5}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(dou(市斗)\right)={\color{rgb(20,165,174)} x}\left(pony\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-2}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.2180147171875 \times 10^{-5}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.2180147171875 \times 10^{-5}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.2180147171875 \times 10^{-5}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-2} = {\color{rgb(20,165,174)} x} \times 2.2180147171875 \times 10^{-5}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancel{10^{-2}}} = {\color{rgb(20,165,174)} x} \times 2.2180147171875 \times {\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-5}}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times 2.2180147171875 \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.2180147171875 \times 10^{-3} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.2180147171875 \times 10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.2180147171875 \times 10^{-3} \times \dfrac{1.0}{2.2180147171875 \times 10^{-3}} = \times \dfrac{1.0}{2.2180147171875 \times 10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.2180147171875}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.2180147171875}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = \dfrac{1.0}{2.2180147171875 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.0}{2.2180147171875 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3}}{2.2180147171875}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx450.85363602\approx4.5085 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(dou(市斗)\right)\approx{\color{rgb(20,165,174)} 4.5085 \times 10^{2}}\left(pony\right)\)
