# Convert ampere • hour to Elementary Charge

Learn how to convert 1 ampere • hour to Elementary Charge step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(ampere \times hour\right)={\color{rgb(20,165,174)} x}\left(Elementary \text{ } Charge\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(coulomb\right)$$
$$\text{Left side: 1.0 } \left(ampere \times hour\right) = {\color{rgb(89,182,91)} 3.6 \times 10^{3}\left(coulomb\right)} = {\color{rgb(89,182,91)} 3.6 \times 10^{3}\left(C\right)}$$
$$\text{Right side: 1.0 } \left(Elementary \text{ } Charge\right) = {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}\left(coulomb\right)} = {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}\left(C\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(ampere \times hour\right)={\color{rgb(20,165,174)} x}\left(Elementary \text{ } Charge\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \times {\color{rgb(89,182,91)} \left(coulomb\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}}} \times {\color{rgb(125,164,120)} \left(coulomb\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \left(C\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}} \cdot {\color{rgb(125,164,120)} \left(C\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 3.6 \times 10^{3}} \cdot {\color{rgb(89,182,91)} \cancel{\left(C\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.602176487 \times 10^{-19}} \times {\color{rgb(125,164,120)} \cancel{\left(C\right)}}$$
$$\text{Conversion Equation}$$
$$3.6 \times 10^{3} = {\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19} = 3.6 \times 10^{3}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{1.602176487 \times 10^{-19}}\right)$$
$${\color{rgb(20,165,174)} x} \times 1.602176487 \times 10^{-19} \times \dfrac{1.0}{1.602176487 \times 10^{-19}} = 3.6 \times 10^{3} \times \dfrac{1.0}{1.602176487 \times 10^{-19}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.602176487}} \times {\color{rgb(99,194,222)} \cancel{10^{-19}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.602176487}} \times {\color{rgb(99,194,222)} \cancel{10^{-19}}}} = 3.6 \times 10^{3} \times \dfrac{1.0}{1.602176487 \times 10^{-19}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{3.6 \times 10^{3}}{1.602176487 \times 10^{-19}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-19}}\text{ can be rewritten to }10^{19}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{19} \times 3.6 \times 10^{3}}{1.602176487}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{22} \times 3.6}{1.602176487}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx2.246943473 \times 10^{22}\approx2.2469 \times 10^{22}$$
$$\text{Conversion Equation}$$
$$1.0\left(ampere \times hour\right)\approx{\color{rgb(20,165,174)} 2.2469 \times 10^{22}}\left(Elementary \text{ } Charge\right)$$

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