# Convert gamma to maru(丸)

Learn how to convert 1 gamma to maru(丸) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(maru(丸)\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(gamma\right) = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(maru(丸)\right) = {\color{rgb(125,164,120)} 30.0\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 30.0\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(maru(丸)\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 30.0}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 30.0} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 30.0} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$10^{-9} = {\color{rgb(20,165,174)} x} \times 30.0$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 30.0 = 10^{-9}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{30.0}\right)$$
$${\color{rgb(20,165,174)} x} \times 30.0 \times \dfrac{1.0}{30.0} = 10^{-9} \times \dfrac{1.0}{30.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{30.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{30.0}}} = 10^{-9} \times \dfrac{1.0}{30.0}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-9}}{30.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx3.3333333333 \times 10^{-11}\approx3.3333 \times 10^{-11}$$
$$\text{Conversion Equation}$$
$$1.0\left(gamma\right)\approx{\color{rgb(20,165,174)} 3.3333 \times 10^{-11}}\left(maru(丸)\right)$$