# Convert last to gamma

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

## Calculation Breakdown

Set up the equation
$$1.0\left(last\right)={\color{rgb(20,165,174)} x}\left(gamma\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(last\right) = {\color{rgb(89,182,91)} 1814.36948\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 1814.36948\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(gamma\right) = {\color{rgb(125,164,120)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(last\right)={\color{rgb(20,165,174)} x}\left(gamma\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 1814.36948} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{-9}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 1814.36948} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{-9}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 1814.36948} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{-9}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$1814.36948 = {\color{rgb(20,165,174)} x} \times 10^{-9}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 10^{-9} = 1814.36948$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{10^{-9}}\right)$$
$${\color{rgb(20,165,174)} x} \times 10^{-9} \times \dfrac{1.0}{10^{-9}} = 1814.36948 \times \dfrac{1.0}{10^{-9}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{-9}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{10^{-9}}}} = 1814.36948 \times \dfrac{1.0}{10^{-9}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1814.36948}{10^{-9}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-9}}\text{ can be rewritten to }10^{9}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = 10^{9} \times 1814.36948$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 1.81436948 \times 10^{12}\approx1.8144 \times 10^{12}$$
$$\text{Conversion Equation}$$
$$1.0\left(last\right)\approx{\color{rgb(20,165,174)} 1.8144 \times 10^{12}}\left(gamma\right)$$