Convert gram / gallon to grain / cubic inch

Learn how to convert 1 gram / gallon to grain / cubic inch step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{g r a m}{g a l l o n}) = x (\frac{g r a i n}{c u b i c i n c h})

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 m}{g a l l o n}) = \frac{1.0}{4.54609} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{1.0}{4.54609} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a i n}{c u b i c i n c h}) = \frac{6.479891}{1.6387064} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{6.479891}{1.6387064} (\frac{k g}{m^{3}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{g r a m}{g a l l o n}) = x (\frac{g r a i n}{c u b i c i n c h})

Insert known values =>

1.0 \times \frac{1.0}{4.54609} \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}{1.6387064} \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{1.0}{4.54609} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{6.479891}{1.6387064} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{1.0}{4.54609} \cdot (\frac{k g}{m^{3}}) = x \times \frac{6.479891}{1.6387064} \times (\frac{k g}{m^{3}})

Conversion Equation

\frac{1.0}{4.54609} = x \times \frac{6.479891}{1.6387064}

Switch sides

x \times \frac{6.479891}{1.6387064} = \frac{1.0}{4.54609}

Isolate

x

Multiply both sides by

(\frac{1.6387064}{6.479891})

x \times \frac{6.479891}{1.6387064} \times \frac{1.6387064}{6.479891} = \frac{1.0}{4.54609} \times \frac{1.6387064}{6.479891}

Cancel

x \times \frac{6.479891 \times 1.6387064}{1.6387064 \times 6.479891} = \frac{1.0 \times 1.6387064}{4.54609 \times 6.479891}

Simplify

x = \frac{1.6387064}{4.54609 \times 6.479891}

Solve

x

x \approx 0.0556282528 \approx 5.5628 \times 10^{- 2}

Conversion Equation

1.0 (\frac{g r a m}{g a l l o n}) \approx 5.5628 \times 10^{- 2} (\frac{g r a i n}{c u b i c i n c h})

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