Convert grain / liter to gram / liter

Learn how to convert 1 grain / liter to gram / liter step by step.

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Calculation Breakdown

Set up the equation

\(1.0\left(\dfrac{grain}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{liter}\right)\)

Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)

\(\text{Left side: 1.0 } \left(\dfrac{grain}{liter}\right) = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Right side: 1.0 } \left(\dfrac{gram}{liter}\right) = {\color{rgb(125,164,120)} 1.0\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} 1.0\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)

\(1.0\left(\dfrac{grain}{liter}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{gram}{liter}\right)\)

\(\text{Insert known values } =>\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.0}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)

\(\text{Or}\)

\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.0} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)

\(\text{Cancel SI units}\)

\(1.0 \times {\color{rgb(89,182,91)} \dfrac{6.479891 \times 10^{-5}}{10^{-3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.0} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)

\(\text{Conversion Equation}\)

\(\dfrac{6.479891 \times 10^{-5}}{10^{-3}} = {\color{rgb(20,165,174)} x} \times 1.0\)

\(\text{Simplify}\)

\(\dfrac{6.479891 \times 10^{-5}}{10^{-3}} = {\color{rgb(20,165,174)} x}\)

Switch sides

\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 10^{-5}}{10^{-3}}\)

Rewrite equation

\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)

\(\text{Rewrite}\)

\({\color{rgb(20,165,174)} x} = 10^{3} \times 6.479891 \times 10^{-5}\)

\(\text{Simplify}\)

\({\color{rgb(20,165,174)} x} = 10^{-2} \times 6.479891\)