# Convert rutherford to curie

Learn how to convert 1 rutherford to curie step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(rutherford\right)={\color{rgb(20,165,174)} x}\left(curie\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(becquerel\right)$$
$$\text{Left side: 1.0 } \left(rutherford\right) = {\color{rgb(89,182,91)} 10^{6}\left(becquerel\right)} = {\color{rgb(89,182,91)} 10^{6}\left(Bq\right)}$$
$$\text{Right side: 1.0 } \left(curie\right) = {\color{rgb(125,164,120)} 3.7 \times 10^{10}\left(becquerel\right)} = {\color{rgb(125,164,120)} 3.7 \times 10^{10}\left(Bq\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(rutherford\right)={\color{rgb(20,165,174)} x}\left(curie\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{6}} \times {\color{rgb(89,182,91)} \left(becquerel\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 3.7 \times 10^{10}}} \times {\color{rgb(125,164,120)} \left(becquerel\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \left(Bq\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 3.7 \times 10^{10}} \cdot {\color{rgb(125,164,120)} \left(Bq\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 10^{6}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Bq\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 3.7 \times 10^{10}} \times {\color{rgb(125,164,120)} \cancel{\left(Bq\right)}}$$
$$\text{Conversion Equation}$$
$$10^{6} = {\color{rgb(20,165,174)} x} \times 3.7 \times 10^{10}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$${\color{rgb(255,204,153)} \cancel{10^{6}}} = {\color{rgb(20,165,174)} x} \times 3.7 \times {\color{rgb(255,204,153)} \cancelto{10^{4}}{10^{10}}}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{3.7 \times 10^{4}}\right)$$
$${\color{rgb(20,165,174)} x} \times 3.7 \times 10^{4} \times \dfrac{1.0}{3.7 \times 10^{4}} = \times \dfrac{1.0}{3.7 \times 10^{4}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{3.7}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{3.7}} \times {\color{rgb(99,194,222)} \cancel{10^{4}}}} = \dfrac{1.0}{3.7 \times 10^{4}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{3.7 \times 10^{4}}$$
Rewrite equation
$$\dfrac{1.0}{10^{4}}\text{ can be rewritten to }10^{-4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-4}}{3.7}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx0.000027027\approx2.7027 \times 10^{-5}$$
$$\text{Conversion Equation}$$
$$1.0\left(rutherford\right)\approx{\color{rgb(20,165,174)} 2.7027 \times 10^{-5}}\left(curie\right)$$