# Convert grain to gamma

Learn how to convert 1 grain to gamma step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(grain\right)={\color{rgb(20,165,174)} x}\left(gamma\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(grain\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(gamma\right) = {\color{rgb(125,164,120)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(grain\right)={\color{rgb(20,165,174)} x}\left(gamma\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-9}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-9}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-9}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$6.479891 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times 10^{-9}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$6.479891 \times {\color{rgb(255,204,153)} \cancel{10^{-5}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{10^{-4}}{10^{-9}}}$$
$$\text{Simplify}$$
$$6.479891 = {\color{rgb(20,165,174)} x} \times 10^{-4}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 10^{-4} = 6.479891$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{10^{-4}}\right)$$
$${\color{rgb(20,165,174)} x} \times 10^{-4} \times \dfrac{1.0}{10^{-4}} = 6.479891 \times \dfrac{1.0}{10^{-4}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-4}}}} = 6.479891 \times \dfrac{1.0}{10^{-4}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{6.479891}{10^{-4}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = 10^{4} \times 6.479891$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 64798.91\approx6.4799 \times 10^{4}$$
$$\text{Conversion Equation}$$
$$1.0\left(grain\right)\approx{\color{rgb(20,165,174)} 6.4799 \times 10^{4}}\left(gamma\right)$$