# Convert curie to rutherford

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

## Calculation Breakdown

Set up the equation
$$1.0\left(curie\right)={\color{rgb(20,165,174)} x}\left(rutherford\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(becquerel\right)$$
$$\text{Left side: 1.0 } \left(curie\right) = {\color{rgb(89,182,91)} 3.7 \times 10^{10}\left(becquerel\right)} = {\color{rgb(89,182,91)} 3.7 \times 10^{10}\left(Bq\right)}$$
$$\text{Right side: 1.0 } \left(rutherford\right) = {\color{rgb(125,164,120)} 10^{6}\left(becquerel\right)} = {\color{rgb(125,164,120)} 10^{6}\left(Bq\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(curie\right)={\color{rgb(20,165,174)} x}\left(rutherford\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} 3.7 \times 10^{10}} \times {\color{rgb(89,182,91)} \left(becquerel\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 10^{6}}} \times {\color{rgb(125,164,120)} \left(becquerel\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} 3.7 \times 10^{10}} \cdot {\color{rgb(89,182,91)} \left(Bq\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 10^{6}} \cdot {\color{rgb(125,164,120)} \left(Bq\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} 3.7 \times 10^{10}} \cdot {\color{rgb(89,182,91)} \cancel{\left(Bq\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 10^{6}} \times {\color{rgb(125,164,120)} \cancel{\left(Bq\right)}}$$
$$\text{Conversion Equation}$$
$$3.7 \times 10^{10} = {\color{rgb(20,165,174)} x} \times 10^{6}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$3.7 \times {\color{rgb(255,204,153)} \cancelto{10^{4}}{10^{10}}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{10^{6}}}$$
$$\text{Simplify}$$
$$3.7 \times 10^{4} = {\color{rgb(20,165,174)} x}$$
Switch sides
$${\color{rgb(20,165,174)} x} = 3.7 \times 10^{4}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 37000 = 3.7 \times 10^{4}$$
$$\text{Conversion Equation}$$
$$1.0\left(curie\right) = {\color{rgb(20,165,174)} 3.7 \times 10^{4}}\left(rutherford\right)$$

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