Convert hogshead to cup

Learn how to convert 1 hogshead to cup step by step.

Calculation Breakdown

Set up the equation
\(1.0\left(hogshead\right)={\color{rgb(20,165,174)} x}\left(cup\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(cubic \text{ } meter\right)\)
\(\text{Left side: 1.0 } \left(hogshead\right) = {\color{rgb(89,182,91)} 2.38480942392 \times 10^{-1}\left(cubic \text{ } meter\right)} = {\color{rgb(89,182,91)} 2.38480942392 \times 10^{-1}\left(m^{3}\right)}\)
\(\text{Right side: 1.0 } \left(cup\right) = {\color{rgb(125,164,120)} 2.5 \times 10^{-4}\left(cubic \text{ } meter\right)} = {\color{rgb(125,164,120)} 2.5 \times 10^{-4}\left(m^{3}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(hogshead\right)={\color{rgb(20,165,174)} x}\left(cup\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 2.38480942392 \times 10^{-1}} \times {\color{rgb(89,182,91)} \left(cubic \text{ } meter\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} 2.5 \times 10^{-4}}} \times {\color{rgb(125,164,120)} \left(cubic \text{ } meter\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 2.38480942392 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \left(m^{3}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} 2.5 \times 10^{-4}} \cdot {\color{rgb(125,164,120)} \left(m^{3}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 2.38480942392 \times 10^{-1}} \cdot {\color{rgb(89,182,91)} \cancel{\left(m^{3}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} 2.5 \times 10^{-4}} \times {\color{rgb(125,164,120)} \cancel{\left(m^{3}\right)}}\)
\(\text{Conversion Equation}\)
\(2.38480942392 \times 10^{-1} = {\color{rgb(20,165,174)} x} \times 2.5 \times 10^{-4}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(2.38480942392 \times {\color{rgb(255,204,153)} \cancel{10^{-1}}} = {\color{rgb(20,165,174)} x} \times 2.5 \times {\color{rgb(255,204,153)} \cancelto{10^{-3}}{10^{-4}}}\)
\(\text{Simplify}\)
\(2.38480942392 = {\color{rgb(20,165,174)} x} \times 2.5 \times 10^{-3}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times 2.5 \times 10^{-3} = 2.38480942392\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.0}{2.5 \times 10^{-3}}\right)\)
\({\color{rgb(20,165,174)} x} \times 2.5 \times 10^{-3} \times \dfrac{1.0}{2.5 \times 10^{-3}} = 2.38480942392 \times \dfrac{1.0}{2.5 \times 10^{-3}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times {\color{rgb(255,204,153)} \cancel{2.5}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}} \times \dfrac{1.0}{{\color{rgb(255,204,153)} \cancel{2.5}} \times {\color{rgb(99,194,222)} \cancel{10^{-3}}}} = 2.38480942392 \times \dfrac{1.0}{2.5 \times 10^{-3}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{2.38480942392}{2.5 \times 10^{-3}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-3}}\text{ can be rewritten to }10^{3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 2.38480942392}{2.5}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx953.92376957\approx9.5392 \times 10^{2}\)
\(\text{Conversion Equation}\)
\(1.0\left(hogshead\right)\approx{\color{rgb(20,165,174)} 9.5392 \times 10^{2}}\left(cup\right)\)

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