# Convert gros to ton

Learn how to convert 1 gros to ton step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(gros\right)={\color{rgb(20,165,174)} x}\left(ton\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(gros\right) = {\color{rgb(89,182,91)} 3.8242264\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 3.8242264\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(ton\right) = {\color{rgb(125,164,120)} 1000.0\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 1000.0\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(gros\right)={\color{rgb(20,165,174)} x}\left(ton\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 3.8242264} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1000.0}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 3.8242264} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1000.0} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 3.8242264} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1000.0} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$3.8242264 = {\color{rgb(20,165,174)} x} \times 10^{3}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 10^{3} = 3.8242264$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{10^{3}}\right)$$
$${\color{rgb(20,165,174)} x} \times 10^{3} \times \dfrac{1.0}{10^{3}} = 3.8242264 \times \dfrac{1.0}{10^{3}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{3}}}} = 3.8242264 \times \dfrac{1.0}{10^{3}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{3.8242264}{10^{3}}$$
Rewrite equation
$$\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = 10^{-3} \times 3.8242264$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 0.0038242264\approx3.8242 \times 10^{-3}$$
$$\text{Conversion Equation}$$
$$1.0\left(gros\right)\approx{\color{rgb(20,165,174)} 3.8242 \times 10^{-3}}\left(ton\right)$$