# Convert gamma to assay ton

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

## Calculation Breakdown

Set up the equation
$$1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(gamma\right) = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{7.0}{2.4 \times 10^{2}}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$10^{-9} = {\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4 \times 10^{2}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4 \times 10^{2}} = 10^{-9}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{2.4 \times 10^{2}}{7.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{7.0}{2.4 \times 10^{2}} \times \dfrac{2.4 \times 10^{2}}{7.0} = 10^{-9} \times \dfrac{2.4 \times 10^{2}}{7.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{7.0}} \times {\color{rgb(99,194,222)} \cancel{2.4}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{2.4}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{7.0}}} = {\color{rgb(255,204,153)} \cancelto{10^{-7}}{10^{-9}}} \times \dfrac{2.4 \times {\color{rgb(255,204,153)} \cancel{10^{2}}}}{7.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-7} \times 2.4}{7.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0000000343\approx3.4286 \times 10^{-8}$$
$$\text{Conversion Equation}$$
$$1.0\left(gamma\right)\approx{\color{rgb(20,165,174)} 3.4286 \times 10^{-8}}\left(assay \text{ } ton\right)$$