Convert rin(厘) to assay ton
Learn how to convert
1
rin(厘) to
assay ton
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(rin(厘)\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(rin(厘)\right) = {\color{rgb(89,182,91)} \dfrac{3.0}{8.0 \times 10^{4}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} \dfrac{3.0}{8.0 \times 10^{4}}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(rin(厘)\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{3.0}{8.0 \times 10^{4}}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{3.0}{8.0 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{3.0}{8.0 \times 10^{4}}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{3.0}{8.0 \times 10^{4}} = {\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4 \times 10^{2}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{3.0}{8.0 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{4}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4 \times {\color{rgb(255,204,153)} \cancel{10^{2}}}}\)
\(\text{Simplify}\)
\(\dfrac{3.0}{8.0 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4} = \dfrac{3.0}{8.0 \times 10^{2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{2.4}{7.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4} \times \dfrac{2.4}{7.0} = \dfrac{3.0}{8.0 \times 10^{2}} \times \dfrac{2.4}{7.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{7.0}} \times {\color{rgb(99,194,222)} \cancel{2.4}}}{{\color{rgb(99,194,222)} \cancel{2.4}} \times {\color{rgb(255,204,153)} \cancel{7.0}}} = \dfrac{3.0 \times 2.4}{8.0 \times 10^{2} \times 7.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{3.0 \times 2.4}{8.0 \times 10^{2} \times 7.0}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 3.0 \times 2.4}{8.0 \times 7.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0012857143\approx1.2857 \times 10^{-3}\)
\(\text{Conversion Equation}\)
\(1.0\left(rin(厘)\right)\approx{\color{rgb(20,165,174)} 1.2857 \times 10^{-3}}\left(assay \text{ } ton\right)\)
