Convert poundal to atomic unit of force
Learn how to convert
1
poundal to
atomic unit of force
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(poundal\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(newton\right)\)
\(\text{Left side: 1.0 } \left(poundal\right) = {\color{rgb(89,182,91)} 0.138254954376\left(newton\right)} = {\color{rgb(89,182,91)} 0.138254954376\left(N\right)}\)
\(\text{Right side: 1.0 } \left(atomic \text{ } unit \text{ } of \text{ } force\right) = {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}\left(newton\right)} = {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}\left(N\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(poundal\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 0.138254954376} \times {\color{rgb(89,182,91)} \left(newton\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}}} \times {\color{rgb(125,164,120)} \left(newton\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 0.138254954376} \cdot {\color{rgb(89,182,91)} \left(N\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}} \cdot {\color{rgb(125,164,120)} \left(N\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 0.138254954376} \cdot {\color{rgb(89,182,91)} \cancel{\left(N\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 8.23872206 \times 10^{-8}} \times {\color{rgb(125,164,120)} \cancel{\left(N\right)}}\)
\(\text{Conversion Equation}\)
\(0.138254954376 = {\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-8} = 0.138254954376\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{8.23872206 \times 10^{-8}}\right)\)
\({\color{rgb(20,165,174)} x} \times 8.23872206 \times 10^{-8} \times \dfrac{1.0}{8.23872206 \times 10^{-8}} = 0.138254954376 \times \dfrac{1.0}{8.23872206 \times 10^{-8}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{8.23872206}} \times {\color{rgb(99,194,222)} \cancel{10^{-8}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{8.23872206}} \times {\color{rgb(99,194,222)} \cancel{10^{-8}}}} = 0.138254954376 \times \dfrac{1.0}{8.23872206 \times 10^{-8}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.138254954376}{8.23872206 \times 10^{-8}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-8}}\text{ can be rewritten to }10^{8}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{8} \times 0.138254954376}{8.23872206}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx1678111.6461\approx1.6781 \times 10^{6}\)
\(\text{Conversion Equation}\)
\(1.0\left(poundal\right)\approx{\color{rgb(20,165,174)} 1.6781 \times 10^{6}}\left(atomic \text{ } unit \text{ } of \text{ } force\right)\)
