Convert carat to shekel
Learn how to convert
1
carat to
shekel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(carat\right)={\color{rgb(20,165,174)} x}\left(shekel\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(carat\right) = {\color{rgb(89,182,91)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(shekel\right) = {\color{rgb(125,164,120)} 1.632932532 \times 10^{-2}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 1.632932532 \times 10^{-2}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(carat\right)={\color{rgb(20,165,174)} x}\left(shekel\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.5919564 \times 10^{-4}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.632932532 \times 10^{-2}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.5919564 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.632932532 \times 10^{-2}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.5919564 \times 10^{-4}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.632932532 \times 10^{-2}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(2.5919564 \times 10^{-4} = {\color{rgb(20,165,174)} x} \times 1.632932532 \times 10^{-2}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(2.5919564 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-4}}} = {\color{rgb(20,165,174)} x} \times 1.632932532 \times {\color{rgb(255,204,153)} \cancel{10^{-2}}}\)
\(\text{Simplify}\)
\(2.5919564 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 1.632932532\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.632932532 = 2.5919564 \times 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.632932532}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.632932532 \times \dfrac{1.0}{1.632932532} = 2.5919564 \times 10^{-2} \times \dfrac{1.0}{1.632932532}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.632932532}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.632932532}}} = 2.5919564 \times 10^{-2} \times \dfrac{1.0}{1.632932532}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.5919564 \times 10^{-2}}{1.632932532}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0158730159\approx1.5873 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(carat\right)\approx{\color{rgb(20,165,174)} 1.5873 \times 10^{-2}}\left(shekel\right)\)
