# Convert assay ton to sack

Learn how to convert 1 assay ton to sack step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(assay \text{ } ton\right)={\color{rgb(20,165,174)} x}\left(sack\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(sack\right) = {\color{rgb(125,164,120)} 45.36\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 45.36\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(assay \text{ } ton\right)={\color{rgb(20,165,174)} x}\left(sack\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 45.36}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 45.36} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 45.36} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{49.0}{1.5 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times 45.36$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 45.36 = \dfrac{49.0}{1.5 \times 10^{3}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{45.36}\right)$$
$${\color{rgb(20,165,174)} x} \times 45.36 \times \dfrac{1.0}{45.36} = \dfrac{49.0}{1.5 \times 10^{3}} \times \dfrac{1.0}{45.36}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{45.36}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{45.36}}} = \dfrac{49.0 \times 1.0}{1.5 \times 10^{3} \times 45.36}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{49.0}{1.5 \times 10^{3} \times 45.36}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 49.0}{1.5 \times 45.36}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0007201646\approx7.2016 \times 10^{-4}$$
$$\text{Conversion Equation}$$
$$1.0\left(assay \text{ } ton\right)\approx{\color{rgb(20,165,174)} 7.2016 \times 10^{-4}}\left(sack\right)$$