# 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 $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx30.612244898\approx30.6122$$
$$\text{Conversion Equation}$$
$$1.0\left({\color{rgb(230,179,255)} kilo}gram\right)\approx{\color{rgb(20,165,174)} 30.6122}\left(assay \text{ } ton\right)$$

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