Convert liang(市兩) to dalton
Learn how to convert
1
liang(市兩) to
dalton
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(liang(市兩)\right)={\color{rgb(20,165,174)} x}\left(dalton\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(liang(市兩)\right) = {\color{rgb(89,182,91)} 5.0 \times 10^{-2}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 5.0 \times 10^{-2}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(dalton\right) = {\color{rgb(125,164,120)} 1.6605390666 \times 10^{-27}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 1.6605390666 \times 10^{-27}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(liang(市兩)\right)={\color{rgb(20,165,174)} x}\left(dalton\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{-2}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.6605390666 \times 10^{-27}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 5.0 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.6605390666 \times 10^{-27}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.6605390666 \times 10^{-27}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(5.0 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 1.6605390666 \times 10^{-27}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(5.0 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} = {\color{rgb(20,165,174)} x} \times 1.6605390666 \times {\color{rgb(255,204,153)} \cancelto{10^{-25}}{10^{-27}}}\)
\(\text{Simplify}\)
\(5.0 = {\color{rgb(20,165,174)} x} \times 1.6605390666 \times 10^{-25}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.6605390666 \times 10^{-25} = 5.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.6605390666 \times 10^{-25}}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.6605390666 \times 10^{-25} \times \dfrac{1.0}{1.6605390666 \times 10^{-25}} = 5.0 \times \dfrac{1.0}{1.6605390666 \times 10^{-25}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.6605390666}} \times {\color{rgb(99,194,222)} \cancel{10^{-25}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.6605390666}} \times {\color{rgb(99,194,222)} \cancel{10^{-25}}}} = 5.0 \times \dfrac{1.0}{1.6605390666 \times 10^{-25}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{5.0}{1.6605390666 \times 10^{-25}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-25}}\text{ can be rewritten to }10^{25}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{25} \times 5.0}{1.6605390666}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3.011070381 \times 10^{25}\approx3.0111 \times 10^{25}\)
\(\text{Conversion Equation}\)
\(1.0\left(liang(市兩)\right)\approx{\color{rgb(20,165,174)} 3.0111 \times 10^{25}}\left(dalton\right)\)
