Convert ounce / fluid-ounce to grain / gallon

Learn how to convert 1 ounce / fluid-ounce to grain / gallon step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{o u n c e}{f l u i d - o u n c e}) = x (\frac{g r a i n}{g a l l o n})

Define the base values of the selected units in relation to the SI unit

(\frac{k i l o g r a m}{c u b i c m e t e r})

Left side: 1.0 (\frac{o u n c e}{f l u i d - o u n c e}) = \frac{2.8349523125}{2.84130625 \times 10^{- 3}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{2.8349523125}{2.84130625 \times 10^{- 3}} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{g a l l o n}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891 \times 10^{- 2}}{3.785411784} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{o u n c e}{f l u i d - o u n c e}) = x (\frac{g r a i n}{g a l l o n})

Insert known values =>

1.0 \times \frac{2.8349523125}{2.84130625 \times 10^{- 3}} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times (\frac{k i l o g r a m}{c u b i c m e t e r})

Or

1.0 \cdot \frac{2.8349523125}{2.84130625 \times 10^{- 3}} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891 \times 10^{- 2}}{3.785411784} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{2.8349523125}{2.84130625 \times 10^{- 3}} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{2.8349523125}{2.84130625 \times 10^{- 3}} = x \times \frac{6.479891 \times 10^{- 2}}{3.785411784}

Switch sides

x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} = \frac{2.8349523125}{2.84130625 \times 10^{- 3}}

Isolate

x

Multiply both sides by

(\frac{3.785411784}{6.479891 \times 10^{- 2}})

x \times \frac{6.479891 \times 10^{- 2}}{3.785411784} \times \frac{3.785411784}{6.479891 \times 10^{- 2}} = \frac{2.8349523125}{2.84130625 \times 10^{- 3}} \times \frac{3.785411784}{6.479891 \times 10^{- 2}}

Cancel

x \times \frac{6.479891 \times 10^{- 2} \times 3.785411784}{3.785411784 \times 6.479891 \times 10^{- 2}} = \frac{2.8349523125 \times 3.785411784}{2.84130625 \times 10^{- 3} \times 6.479891 \times 10^{- 2}}

Simplify

x = \frac{2.8349523125 \times 3.785411784}{2.84130625 \times 10^{- 3} \times 6.479891 \times 10^{- 2}}

Rewrite equation

\frac{1.0}{10^{- 3}} can be rewritten to 10^{3}

\frac{1.0}{10^{- 2}} can be rewritten to 10^{2}

Rewrite

x = \frac{10^{3} \times 10^{2} \times 2.8349523125 \times 3.785411784}{2.84130625 \times 6.479891}

Simplify

x = \frac{10^{5} \times 2.8349523125 \times 3.785411784}{2.84130625 \times 6.479891}

Solve

x

x \approx 58287.192924 \approx 5.8287 \times 10^{4}

Conversion Equation

1.0 (\frac{o u n c e}{f l u i d - o u n c e}) \approx 5.8287 \times 10^{4} (\frac{g r a i n}{g a l l o n})

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