# Convert kibi to pebi

Learn how to convert 1 kibi to pebi step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(kibi\right)={\color{rgb(20,165,174)} x}\left(pebi\right)$$
Define the prefix value(s)
$$The \text{ } value \text{ } of \text{ } kibi \text{ } is \text{ } 2.0^{10}$$
$$The \text{ } value \text{ } of \text{ } pebi \text{ } is \text{ } 2.0^{50}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(kibi\right)={\color{rgb(20,165,174)} x}\left(pebi\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 2.0^{10}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0^{50}}}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 2.0^{10}} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0^{50}}$$
$$\text{Conversion Equation}$$
$$2.0^{10} = {\color{rgb(20,165,174)} x} \times 2.0^{50}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{2.0^{10}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancelto{2^{40}}{2.0^{50}}}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 2^{40}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2^{40} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2^{40}}\right)$$
$${\color{rgb(20,165,174)} x} \times 2^{40} \times \dfrac{1.0}{2^{40}} = \times \dfrac{1.0}{2^{40}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2^{40}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2^{40}}}} = \dfrac{1.0}{2^{40}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{2^{40}}$$
Rewrite equation
$$\dfrac{1.0}{2^{40}}\text{ can be rewritten to }2^{-40}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = 2^{-40}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx9.0949470177 \times 10^{-13}\approx9.0949 \times 10^{-13}$$
$$\text{Conversion Equation}$$
$$1.0\left(kibi\right)\approx{\color{rgb(20,165,174)} 9.0949 \times 10^{-13}}\left(pebi\right)$$