Convert mark to carat
Learn how to convert
1
mark to
carat
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(mark\right)={\color{rgb(20,165,174)} x}\left(carat\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(mark\right) = {\color{rgb(89,182,91)} 0.2488278144\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 0.2488278144\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(carat\right) = {\color{rgb(125,164,120)} 2.0 \times 10^{-4}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 2.0 \times 10^{-4}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(mark\right)={\color{rgb(20,165,174)} x}\left(carat\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 0.2488278144} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.0 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 0.2488278144} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.0 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 0.2488278144} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.0 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(0.2488278144 = {\color{rgb(20,165,174)} x} \times 2.0 \times 10^{-4}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.0 \times 10^{-4} = 0.2488278144\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.0 \times 10^{-4}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.0 \times 10^{-4} \times \dfrac{1.0}{2.0 \times 10^{-4}} = 0.2488278144 \times \dfrac{1.0}{2.0 \times 10^{-4}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.0}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.0}} \times {\color{rgb(99,194,222)} \cancel{10^{-4}}}} = 0.2488278144 \times \dfrac{1.0}{2.0 \times 10^{-4}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.2488278144}{2.0 \times 10^{-4}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-4}}\text{ can be rewritten to }10^{4}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 0.2488278144}{2.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 1244.139072\approx1.2441 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(mark\right)\approx{\color{rgb(20,165,174)} 1.2441 \times 10^{3}}\left(carat\right)\)
