Convert sheet to international unit
Learn how to convert
1
sheet to
international unit
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(sheet\right)={\color{rgb(20,165,174)} x}\left(international \text{ } unit\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(sheet\right) = {\color{rgb(89,182,91)} 6.479891 \times 10^{-4}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 6.479891 \times 10^{-4}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(international \text{ } unit\right) = {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(sheet\right)={\color{rgb(20,165,174)} x}\left(international \text{ } unit\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 6.479891 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 6.479891 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10^{-6}}{660.0}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(6.479891 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-6}}{660.0}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(6.479891 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-6}}}}{660.0}\)
\(\text{Simplify}\)
\(6.479891 = {\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{660.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{660.0} = 6.479891\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{660.0}{10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10^{-2}}{660.0} \times \dfrac{660.0}{10^{-2}} = 6.479891 \times \dfrac{660.0}{10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10^{-2}}} \times {\color{rgb(99,194,222)} \cancel{660.0}}}{{\color{rgb(99,194,222)} \cancel{660.0}} \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}} = 6.479891 \times \dfrac{660.0}{10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{6.479891 \times 660.0}{10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = 10^{2} \times 6.479891 \times 660.0\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 427672.806\approx4.2767 \times 10^{5}\)
\(\text{Conversion Equation}\)
\(1.0\left(sheet\right)\approx{\color{rgb(20,165,174)} 4.2767 \times 10^{5}}\left(international \text{ } unit\right)\)
