Convert qian(市钱) to pennyweight
Learn how to convert
1
qian(市钱) to
pennyweight
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(qian(市钱)\right)={\color{rgb(20,165,174)} x}\left(pennyweight\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(qian(市钱)\right) = {\color{rgb(89,182,91)} 5.0 \times 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 5.0 \times 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(pennyweight\right) = {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(qian(市钱)\right)={\color{rgb(20,165,174)} x}\left(pennyweight\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{-3}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 5.0 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 5.0 \times 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.55517384 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(5.0 \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 1.55517384 \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(5.0 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}} = {\color{rgb(20,165,174)} x} \times 1.55517384 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(5.0 = {\color{rgb(20,165,174)} x} \times 1.55517384\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.55517384 = 5.0\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.55517384}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.55517384 \times \dfrac{1.0}{1.55517384} = 5.0 \times \dfrac{1.0}{1.55517384}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.55517384}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.55517384}}} = 5.0 \times \dfrac{1.0}{1.55517384}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{5.0}{1.55517384}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx3.2150746569\approx3.2151\)
\(\text{Conversion Equation}\)
\(1.0\left(qian(市钱)\right)\approx{\color{rgb(20,165,174)} 3.2151}\left(pennyweight\right)\)
