Convert mic to assay ton

Learn how to convert 1 mic to assay ton step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(mic\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(mic\right) = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(mic\right)={\color{rgb(20,165,174)} x}\left(assay \text{ } ton\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{49.0}{1.5 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-9} = {\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}} = 10^{-9}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.5 \times 10^{3}}{49.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{49.0}{1.5 \times 10^{3}} \times \dfrac{1.5 \times 10^{3}}{49.0} = 10^{-9} \times \dfrac{1.5 \times 10^{3}}{49.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{49.0}} \times {\color{rgb(99,194,222)} \cancel{1.5}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{1.5}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{49.0}}} = {\color{rgb(255,204,153)} \cancelto{10^{-6}}{10^{-9}}} \times \dfrac{1.5 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}{49.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-6} \times 1.5}{49.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000306\approx3.0612 \times 10^{-8}\)
\(\text{Conversion Equation}\)
\(1.0\left(mic\right)\approx{\color{rgb(20,165,174)} 3.0612 \times 10^{-8}}\left(assay \text{ } ton\right)\)

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