Convert grain / gallon to grain / fluid-ounce

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

Calculation Breakdown

Set up the equation

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

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{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}})

Right side: 1.0 (\frac{g r a i n}{f l u i d - o u n c e}) = \frac{6.479891}{2.84130625} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{2.84130625} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

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

Cancel SI units

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

Conversion Equation

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

Cancel factors on both sides

Cancel factors

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

Simplify

\frac{10^{- 2}}{3.785411784} = x \times \frac{1.0}{2.84130625}

Switch sides

x \times \frac{1.0}{2.84130625} = \frac{10^{- 2}}{3.785411784}

Isolate

x

Multiply both sides by

(\frac{2.84130625}{1.0})

x \times \frac{1.0}{2.84130625} \times \frac{2.84130625}{1.0} = \frac{10^{- 2}}{3.785411784} \times \frac{2.84130625}{1.0}

Cancel

x \times \frac{1.0 \times 2.84130625}{2.84130625 \times 1.0} = \frac{10^{- 2} \times 2.84130625}{3.785411784 \times 1.0}

Simplify

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

Solve

x

x \approx 0.007505937 \approx 7.5059 \times 10^{- 3}

Conversion Equation

1.0 (\frac{g r a i n}{g a l l o n}) \approx 7.5059 \times 10^{- 3} (\frac{g r a i n}{f l u i d - o u n c e})

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