Convert dessertspoon to diesel
Learn how to convert
1
dessertspoon to
diesel
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(dessertspoon\right)={\color{rgb(20,165,174)} x}\left(diesel\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(dessertspoon\right) = {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(diesel\right) = {\color{rgb(125,164,120)} \dfrac{10.0}{8.5}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} \dfrac{10.0}{8.5}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(dessertspoon\right)={\color{rgb(20,165,174)} x}\left(diesel\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{10.0}{8.5}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{10.0}{8.5}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{10.0}{8.5}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(1.18387760416667 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times \dfrac{10.0}{8.5}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{10.0}{8.5} = 1.18387760416667 \times 10^{-5}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{8.5}{10.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{10.0}{8.5} \times \dfrac{8.5}{10.0} = 1.18387760416667 \times 10^{-5} \times \dfrac{8.5}{10.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{10.0}} \times {\color{rgb(99,194,222)} \cancel{8.5}}}{{\color{rgb(99,194,222)} \cancel{8.5}} \times {\color{rgb(255,204,153)} \cancel{10.0}}} = 1.18387760416667 \times 10^{-5} \times \dfrac{8.5}{10.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.18387760416667 \times 10^{-5} \times 8.5}{10.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.000010063\approx1.0063 \times 10^{-5}\)
\(\text{Conversion Equation}\)
\(1.0\left(dessertspoon\right)\approx{\color{rgb(20,165,174)} 1.0063 \times 10^{-5}}\left(diesel\right)\)
