Convert international unit to ounce
Learn how to convert
1
international unit to
ounce
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(international \text{ } unit\right)={\color{rgb(20,165,174)} x}\left(ounce\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(international \text{ } unit\right) = {\color{rgb(89,182,91)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} \dfrac{10^{-6}}{660.0}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(ounce\right) = {\color{rgb(125,164,120)} 5.0 \times 10^{-2}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 5.0 \times 10^{-2}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(international \text{ } unit\right)={\color{rgb(20,165,174)} x}\left(ounce\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-6}}{660.0}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 5.0 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{-6}}{660.0}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 5.0 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{-6}}{660.0}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 5.0 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{-6}}{660.0} = {\color{rgb(20,165,174)} x} \times 5.0 \times 10^{-2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{{\color{rgb(255,204,153)} \cancelto{10^{-4}}{10^{-6}}}}{660.0} = {\color{rgb(20,165,174)} x} \times 5.0 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}\)
\(\text{Simplify}\)
\(\dfrac{10^{-4}}{660.0} = {\color{rgb(20,165,174)} x} \times 5.0\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 5.0 = \dfrac{10^{-4}}{660.0}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times 5.0 \times \dfrac{1.0}{5.0} = \dfrac{10^{-4}}{660.0} \times \dfrac{1.0}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{5.0}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{5.0}}} = \dfrac{10^{-4} \times 1.0}{660.0 \times 5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-4}}{660.0 \times 5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000000303\approx3.0303 \times 10^{-8}\)
\(\text{Conversion Equation}\)
\(1.0\left(international \text{ } unit\right)\approx{\color{rgb(20,165,174)} 3.0303 \times 10^{-8}}\left(ounce\right)\)
