Convert foot-poundal to atomic unit of energy
Learn how to convert
1
foot-poundal to
atomic unit of energy
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(foot-poundal\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } energy\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(joule\right)\)
\(\text{Left side: 1.0 } \left(foot-poundal\right) = {\color{rgb(89,182,91)} 4.21401100938048 \times 10^{-2}\left(joule\right)} = {\color{rgb(89,182,91)} 4.21401100938048 \times 10^{-2}\left(J\right)}\)
\(\text{Right side: 1.0 } \left(atomic \text{ } unit \text{ } of \text{ } energy\right) = {\color{rgb(125,164,120)} 4.359744 \times 10^{-18}\left(joule\right)} = {\color{rgb(125,164,120)} 4.359744 \times 10^{-18}\left(J\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(foot-poundal\right)={\color{rgb(20,165,174)} x}\left(atomic \text{ } unit \text{ } of \text{ } energy\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 4.21401100938048 \times 10^{-2}} \times {\color{rgb(89,182,91)} \left(joule\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 4.359744 \times 10^{-18}}} \times {\color{rgb(125,164,120)} \left(joule\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 4.21401100938048 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \left(J\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 4.359744 \times 10^{-18}} \cdot {\color{rgb(125,164,120)} \left(J\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 4.21401100938048 \times 10^{-2}} \cdot {\color{rgb(89,182,91)} \cancel{\left(J\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 4.359744 \times 10^{-18}} \times {\color{rgb(125,164,120)} \cancel{\left(J\right)}}\)
\(\text{Conversion Equation}\)
\(4.21401100938048 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 4.359744 \times 10^{-18}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(4.21401100938048 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}} = {\color{rgb(20,165,174)} x} \times 4.359744 \times {\color{rgb(255,204,153)} \cancelto{10^{-16}}{10^{-18}}}\)
\(\text{Simplify}\)
\(4.21401100938048 = {\color{rgb(20,165,174)} x} \times 4.359744 \times 10^{-16}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 4.359744 \times 10^{-16} = 4.21401100938048\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{4.359744 \times 10^{-16}}\right)\)
\({\color{rgb(20,165,174)} x} \times 4.359744 \times 10^{-16} \times \dfrac{1.0}{4.359744 \times 10^{-16}} = 4.21401100938048 \times \dfrac{1.0}{4.359744 \times 10^{-16}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{4.359744}} \times {\color{rgb(99,194,222)} \cancel{10^{-16}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{4.359744}} \times {\color{rgb(99,194,222)} \cancel{10^{-16}}}} = 4.21401100938048 \times \dfrac{1.0}{4.359744 \times 10^{-16}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{4.21401100938048}{4.359744 \times 10^{-16}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-16}}\text{ can be rewritten to }10^{16}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{16} \times 4.21401100938048}{4.359744}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx9.6657303947 \times 10^{15}\approx9.6657 \times 10^{15}\)
\(\text{Conversion Equation}\)
\(1.0\left(foot-poundal\right)\approx{\color{rgb(20,165,174)} 9.6657 \times 10^{15}}\left(atomic \text{ } unit \text{ } of \text{ } energy\right)\)
