Convert Shaku(勺) to cong
Learn how to convert
1
Shaku(勺) to
cong
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(Shaku(勺)\right)={\color{rgb(20,165,174)} x}\left(cong\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(square \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(Shaku(勺)\right) = {\color{rgb(89,182,91)} \dfrac{4.0}{121.0}\left(square \text{ } meter\right)} = {\color{rgb(89,182,91)} \dfrac{4.0}{121.0}\left(m^{2}\right)}\)
\(\text{Right side: 1.0 } \left(cong\right) = {\color{rgb(125,164,120)} 10^{3}\left(square \text{ } meter\right)} = {\color{rgb(125,164,120)} 10^{3}\left(m^{2}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(Shaku(勺)\right)={\color{rgb(20,165,174)} x}\left(cong\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.0}{121.0}} \times {\color{rgb(89,182,91)} \left(square \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{3}}} \times {\color{rgb(125,164,120)} \left(square \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{4.0}{121.0}} \cdot {\color{rgb(89,182,91)} \left(m^{2}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{3}} \cdot {\color{rgb(125,164,120)} \left(m^{2}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{4.0}{121.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{2}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{3}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{2}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{4.0}{121.0} = {\color{rgb(20,165,174)} x} \times 10^{3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 10^{3} = \dfrac{4.0}{121.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{10^{3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 10^{3} \times \dfrac{1.0}{10^{3}} = \dfrac{4.0}{121.0} \times \dfrac{1.0}{10^{3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{3}}}} = \dfrac{4.0 \times 1.0}{121.0 \times 10^{3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.0}{121.0 \times 10^{3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 4.0}{121.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000330579\approx3.3058 \times 10^{-5}\)
\(\text{Conversion Equation}\)
\(1.0\left(Shaku(勺)\right)\approx{\color{rgb(20,165,174)} 3.3058 \times 10^{-5}}\left(cong\right)\)
