# Convert pony to firkin

Learn how to convert 1 pony to firkin step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(pony\right)={\color{rgb(20,165,174)} x}\left(firkin\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(cubic \text{ } meter\right)$$
$$\text{Left side: 1.0 } \left(pony\right) = {\color{rgb(89,182,91)} 2.2180147171875 \times 10^{-5}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 2.2180147171875 \times 10^{-5}\left(m^{3}\right)}$$
$$\text{Right side: 1.0 } \left(firkin\right) = {\color{rgb(125,164,120)} 3.4068706056 \times 10^{-2}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 3.4068706056 \times 10^{-2}\left(m^{3}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(pony\right)={\color{rgb(20,165,174)} x}\left(firkin\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 2.2180147171875 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.4068706056 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 2.2180147171875 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.4068706056 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 2.2180147171875 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.4068706056 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}$$
$$\text{Conversion Equation}$$
$$2.2180147171875 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times 3.4068706056 \times 10^{-2}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$2.2180147171875 \times {\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times 3.4068706056 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}$$
$$\text{Simplify}$$
$$2.2180147171875 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 3.4068706056$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 3.4068706056 = 2.2180147171875 \times 10^{-3}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{3.4068706056}\right)$$
$${\color{rgb(20,165,174)} x} \times 3.4068706056 \times \dfrac{1.0}{3.4068706056} = 2.2180147171875 \times 10^{-3} \times \dfrac{1.0}{3.4068706056}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.4068706056}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.4068706056}}} = 2.2180147171875 \times 10^{-3} \times \dfrac{1.0}{3.4068706056}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{2.2180147171875 \times 10^{-3}}{3.4068706056}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.0006510417\approx6.5104 \times 10^{-4}$$
$$\text{Conversion Equation}$$
$$1.0\left(pony\right)\approx{\color{rgb(20,165,174)} 6.5104 \times 10^{-4}}\left(firkin\right)$$