Convert diesel to drop
Learn how to convert
1
diesel to
drop
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(diesel\right)={\color{rgb(20,165,174)} x}\left(drop\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(diesel\right) = {\color{rgb(89,182,91)} \dfrac{10.0}{8.5}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} \dfrac{10.0}{8.5}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(drop\right) = {\color{rgb(125,164,120)} 7.78866844846491 \times 10^{-8}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 7.78866844846491 \times 10^{-8}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(diesel\right)={\color{rgb(20,165,174)} x}\left(drop\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10.0}{8.5}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 7.78866844846491 \times 10^{-8}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10.0}{8.5}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 7.78866844846491 \times 10^{-8}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10.0}{8.5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 7.78866844846491 \times 10^{-8}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10.0}{8.5} = {\color{rgb(20,165,174)} x} \times 7.78866844846491 \times 10^{-8}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 7.78866844846491 \times 10^{-8} = \dfrac{10.0}{8.5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{7.78866844846491 \times 10^{-8}}\right)\)
\({\color{rgb(20,165,174)} x} \times 7.78866844846491 \times 10^{-8} \times \dfrac{1.0}{7.78866844846491 \times 10^{-8}} = \dfrac{10.0}{8.5} \times \dfrac{1.0}{7.78866844846491 \times 10^{-8}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{7.78866844846491}} \times {\color{rgb(99,194,222)} \cancel{10^{-8}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{7.78866844846491}} \times {\color{rgb(99,194,222)} \cancel{10^{-8}}}} = \dfrac{10.0 \times 1.0}{8.5 \times 7.78866844846491 \times 10^{-8}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0}{8.5 \times 7.78866844846491 \times 10^{-8}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-8}}\text{ can be rewritten to }10^{8}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{8} \times 10.0}{8.5 \times 7.78866844846491}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0^{9}}{8.5 \times 7.78866844846491}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx15104900.1\approx1.5105 \times 10^{7}\)
\(\text{Conversion Equation}\)
\(1.0\left(diesel\right)\approx{\color{rgb(20,165,174)} 1.5105 \times 10^{7}}\left(drop\right)\)
