Convert to(升) to koku(石)
Learn how to convert
1
to(升) to
koku(石)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(to(升)\right)={\color{rgb(20,165,174)} x}\left(koku(石)\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(to(升)\right) = {\color{rgb(89,182,91)} \dfrac{2.401}{1.331 \times 10^{2}}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} \dfrac{2.401}{1.331 \times 10^{2}}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(koku(石)\right) = {\color{rgb(125,164,120)} \dfrac{2401.0}{1.331 \times 10^{4}}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} \dfrac{2401.0}{1.331 \times 10^{4}}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(to(升)\right)={\color{rgb(20,165,174)} x}\left(koku(石)\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.401}{1.331 \times 10^{2}}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2401.0}{1.331 \times 10^{4}}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{2.401}{1.331 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2401.0}{1.331 \times 10^{4}}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{2.401}{1.331 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2401.0}{1.331 \times 10^{4}}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{2.401}{1.331 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{2401.0}{1.331 \times 10^{4}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{2.401}{{\color{rgb(255,204,153)} \cancel{1.331}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2401.0}{{\color{rgb(255,204,153)} \cancel{1.331}} \times {\color{rgb(99,194,222)} \cancelto{10^{2}}{10^{4}}}}\)
\(\text{Simplify}\)
\(2.401 = {\color{rgb(20,165,174)} x} \times \dfrac{2401.0}{10^{2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2401.0}{10^{2}} = 2.401\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{10^{2}}{2401.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2401.0}{10^{2}} \times \dfrac{10^{2}}{2401.0} = 2.401 \times \dfrac{10^{2}}{2401.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2401.0}} \times {\color{rgb(99,194,222)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{2401.0}}} = 2.401 \times \dfrac{10^{2}}{2401.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.401 \times 10^{2}}{2401.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 0.1 = 0.001 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(to(升)\right) = {\color{rgb(20,165,174)} 0.001 \times 10^{2}}\left(koku(石)\right)\)
