Convert gamma to carat
Learn how to convert
1
gamma to
carat
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(carat\right)\)
Define the base values of the selected units in relation to the SI unit \(\left({\color{rgb(230,179,255)} kilo}gram\right)\)
\(\text{Left side: 1.0 } \left(gamma\right) = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(89,182,91)} 10^{-9}\left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Right side: 1.0 } \left(carat\right) = {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}\left({\color{rgb(230,179,255)} k}g\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(gamma\right)={\color{rgb(20,165,174)} x}\left(carat\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \times {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} kilo}gram\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} kilo}gram\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \left({\color{rgb(230,179,255)} k}g\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left({\color{rgb(230,179,255)} k}g\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 10^{-9}} \cdot {\color{rgb(89,182,91)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.5919564 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left({\color{rgb(230,179,255)} k}g\right)}}\)
\(\text{Conversion Equation}\)
\(10^{-9} = {\color{rgb(20,165,174)} x} \times 2.5919564 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\({\color{rgb(255,204,153)} \cancelto{10^{-5}}{10^{-9}}} = {\color{rgb(20,165,174)} x} \times 2.5919564 \times {\color{rgb(255,204,153)} \cancel{10^{-4}}}\)
\(\text{Simplify}\)
\(10^{-5} = {\color{rgb(20,165,174)} x} \times 2.5919564\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.5919564 = 10^{-5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.5919564}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.5919564 \times \dfrac{1.0}{2.5919564} = 10^{-5} \times \dfrac{1.0}{2.5919564}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.5919564}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.5919564}}} = 10^{-5} \times \dfrac{1.0}{2.5919564}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-5}}{2.5919564}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000038581\approx3.8581 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(gamma\right)\approx{\color{rgb(20,165,174)} 3.8581 \times 10^{-6}}\left(carat\right)\)
