Convert grain / gallon to pound / fluid-ounce

Learn how to convert 1 grain / gallon to pound / 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{p o u n d}{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}{454.609} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{454.609} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{p o u n d}{f l u i d - o u n c e}) = \frac{5.0}{2.95735295625 \times 10^{- 4}} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{5.0}{2.95735295625 \times 10^{- 4}} (\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{p o u n d}{f l u i d - o u n c e})

Insert known values =>

1.0 \times \frac{6.479891}{454.609} \times (\frac{k i l o g r a m}{c u b i c m e t e r}) = x \times \frac{5.0}{2.95735295625 \times 10^{- 4}} \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}{454.609} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{5.0}{2.95735295625 \times 10^{- 4}} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{6.479891}{454.609} \cdot (\frac{k g}{m^{3}}) = x \times \frac{5.0}{2.95735295625 \times 10^{- 4}} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{6.479891}{454.609} = x \times \frac{5.0}{2.95735295625 \times 10^{- 4}}

Switch sides

x \times \frac{5.0}{2.95735295625 \times 10^{- 4}} = \frac{6.479891}{454.609}

Isolate

x

Multiply both sides by

(\frac{2.95735295625 \times 10^{- 4}}{5.0})

x \times \frac{5.0}{2.95735295625 \times 10^{- 4}} \times \frac{2.95735295625 \times 10^{- 4}}{5.0} = \frac{6.479891}{454.609} \times \frac{2.95735295625 \times 10^{- 4}}{5.0}

Cancel

x \times \frac{5.0 \times 2.95735295625 \times 10^{- 4}}{2.95735295625 \times 10^{- 4} \times 5.0} = \frac{6.479891 \times 2.95735295625 \times 10^{- 4}}{454.609 \times 5.0}

Simplify

x = \frac{6.479891 \times 2.95735295625 \times 10^{- 4}}{454.609 \times 5.0}

Solve

x

x \approx 0.0000008431 \approx 8.4307 \times 10^{- 7}

Conversion Equation

1.0 (\frac{g r a i n}{g a l l o n}) \approx 8.4307 \times 10^{- 7} (\frac{p o u n d}{f l u i d - o u n c e})

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