Convert dessertspoon to quart
Learn how to convert
1
dessertspoon to
quart
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(dessertspoon\right)={\color{rgb(20,165,174)} x}\left(quart\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(dessertspoon\right) = {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(quart\right) = {\color{rgb(125,164,120)} 1.1365225 \times 10^{-3}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 1.1365225 \times 10^{-3}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(dessertspoon\right)={\color{rgb(20,165,174)} x}\left(quart\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 1.1365225 \times 10^{-3}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 1.1365225 \times 10^{-3}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1.18387760416667 \times 10^{-5}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 1.1365225 \times 10^{-3}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(1.18387760416667 \times 10^{-5} = {\color{rgb(20,165,174)} x} \times 1.1365225 \times 10^{-3}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(1.18387760416667 \times {\color{rgb(255,204,153)} \cancelto{10^{-2}}{10^{-5}}} = {\color{rgb(20,165,174)} x} \times 1.1365225 \times {\color{rgb(255,204,153)} \cancel{10^{-3}}}\)
\(\text{Simplify}\)
\(1.18387760416667 \times 10^{-2} = {\color{rgb(20,165,174)} x} \times 1.1365225\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 1.1365225 = 1.18387760416667 \times 10^{-2}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{1.1365225}\right)\)
\({\color{rgb(20,165,174)} x} \times 1.1365225 \times \dfrac{1.0}{1.1365225} = 1.18387760416667 \times 10^{-2} \times \dfrac{1.0}{1.1365225}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{1.1365225}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{1.1365225}}} = 1.18387760416667 \times 10^{-2} \times \dfrac{1.0}{1.1365225}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1.18387760416667 \times 10^{-2}}{1.1365225}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0104166667\approx1.0417 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(dessertspoon\right)\approx{\color{rgb(20,165,174)} 1.0417 \times 10^{-2}}\left(quart\right)\)
