Convert kilogram to assay ton
Learn how to convert
1
kilogram to
assay ton
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left({\color{rgb(230,179,255)} kilo}gram\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(gram\right) = {\color{rgb(89,182,91)} 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} k}g\right)}\)
Define the values of the selected prefixes
\(\text{Left side: } kilo = k = {\color{rgb(250,175,0)} 10^{3}}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left({\color{rgb(230,179,255)} kilo}gram\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(10^{3} \times 10^{-3} = {\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}}\)
\(\text{Simplify}\)
\(1.0 = {\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}} = 1.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.5 \times 10^{3}}{49.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}} \times \dfrac{1.5 \times 10^{3}}{49.0} = 1.0 \times \dfrac{1.5 \times 10^{3}}{49.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{49.0}} \times {\color{rgb(99,194,222)} \cancel{1.5}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{1.5}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{49.0}}} = 1.0 \times \dfrac{1.5 \times 10^{3}}{49.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.5 \times 10^{3}}{49.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx30.612244898\approx30.6122\)
\(\text{Conversion Equation}\)
\(1.0\left({\color{rgb(230,179,255)} kilo}gram\right)\approx{\color{rgb(20,165,174)} 30.6122}\left(assay \text{ } ton\right)\)
