Convert assay ton to international unit
Learn how to convert
1
assay ton to
international unit
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(assay \text{ } ton\right)={\color{rgb(20,165,174)} x}\left(international \text{ } unit\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(assay \text{ } ton\right) = {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(international \text{ } unit\right) = {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(assay \text{ } ton\right)={\color{rgb(20,165,174)} x}\left(international \text{ } unit\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{49.0}{1.5 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{49.0}{1.5 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-6}}{660.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-6}}{660.0} = \dfrac{49.0}{1.5 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{660.0}{10^{-6}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-6}}{660.0} \times \dfrac{660.0}{10^{-6}} = \dfrac{49.0}{1.5 \times 10^{3}} \times \dfrac{660.0}{10^{-6}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-6}}} \times {\color{rgb(99,194,222)} \cancel{660.0}}}{{\color{rgb(99,194,222)} \cancel{660.0}} \times {\color{rgb(255,204,153)} \cancel{10^{-6}}}} = \dfrac{49.0 \times 660.0}{1.5 \times {\color{rgb(255,204,153)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-6}}}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{49.0 \times 660.0}{1.5 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 49.0 \times 660.0}{1.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 21560000 = 2.156 \times 10^{7}\)
\(\text{Conversion Equation}\)
\(1.0\left(assay \text{ } ton\right) = {\color{rgb(20,165,174)} 2.156 \times 10^{7}}\left(international \text{ } unit\right)\)
