Convert kilogram to carat

Learn how to convert 1 kilogram to carat step by step.

Calculation Breakdown

Set up the equation
$$1.0\left({\color{rgb(230,179,255)} kilo}gram\right)={\color{rgb(20,165,174)} x}\left(carat\right)$$
Define the base values of the selected units in relation to the SI unit $$\left({\color{rgb(230,179,255)} kilo}gram\right)$$
$$\text{Left side: 1.0 } \left(gram\right) = {\color{rgb(89,182,91)} 10^{-3}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-3}\left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Right side: 1.0 } \left(carat\right) = {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} k}g\right)}$$
Define the values of the selected prefixes
$$\text{Left side: } kilo = k = {\color{rgb(250,175,0)} 10^{3}}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left({\color{rgb(230,179,255)} kilo}gram\right)={\color{rgb(20,165,174)} x}\left(carat\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(250,175,0)} 10^{3}} \times {\color{rgb(89,182,91)} 10^{-3}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}$$
$$\text{Conversion Equation}$$
$$10^{3} \times 10^{-3} = {\color{rgb(20,165,174)} x} \times 2.5919564 \times 10^{-4}$$
$$\text{Simplify}$$
$$1.0 = {\color{rgb(20,165,174)} x} \times 2.5919564 \times 10^{-4}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times 2.5919564 \times 10^{-4} = 1.0$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{1.0}{2.5919564 \times 10^{-4}}\right)$$
$${\color{rgb(20,165,174)} x} \times 2.5919564 \times 10^{-4} \times \dfrac{1.0}{2.5919564 \times 10^{-4}} = 1.0 \times \dfrac{1.0}{2.5919564 \times 10^{-4}}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.5919564}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.5919564}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}}} = 1.0 \times \dfrac{1.0}{2.5919564 \times 10^{-4}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1.0}{2.5919564 \times 10^{-4}}$$
Rewrite equation
$$\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{4}}{2.5919564}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x}\approx3858.0895882\approx3.8581 \times 10^{3}$$
$$\text{Conversion Equation}$$
$$1.0\left({\color{rgb(230,179,255)} kilo}gram\right)\approx{\color{rgb(20,165,174)} 3.8581 \times 10^{3}}\left(carat\right)$$