Convert kilogram / cubic meter to gram / cubic meter

Learn how to convert 1 kilogram / cubic meter to gram / cubic meter step by step.

Calculation Breakdown

Set up the equation

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

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}{c u b i c m e t e r}) = 10^{- 3} (\frac{k i l o g r a m}{c u b i c m e t e r}) = 10^{- 3} (\frac{k g}{m^{3}})

Right side: 1.0 (\frac{g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{7.64554857984} (\frac{k i l o g r a m}{c u b i c m e t e r}) = \frac{10^{- 2}}{7.64554857984} (\frac{k g}{m^{3}})

Define the values of the selected prefixes

Left side: \frac{k i l o}{1.0} = \frac{k}{1.0} = \frac{10^{3}}{1.0}

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times \frac{10^{3}}{1.0} \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{10^{- 2}}{7.64554857984} \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{10^{3}}{1.0} \times 10^{- 3} \cdot (\frac{k g}{m^{3}}) = x \cdot \frac{10^{- 2}}{7.64554857984} \cdot (\frac{k g}{m^{3}})

Cancel SI units

1.0 \times \frac{10^{3}}{1.0} \times 10^{- 3} \cdot (\frac{k g}{m^{3}}) = x \times \frac{10^{- 2}}{7.64554857984} \times (\frac{k g}{m^{3}})

Conversion Equation

10^{- 3} \times \frac{10^{3}}{1.0} = x \times \frac{10^{- 2}}{7.64554857984}

Simplify

1.0 = x \times \frac{10^{- 2}}{7.64554857984}

Switch sides

x \times \frac{10^{- 2}}{7.64554857984} = 1.0

Isolate

x

Multiply both sides by

(\frac{7.64554857984}{10^{- 2}})

x \times \frac{10^{- 2}}{7.64554857984} \times \frac{7.64554857984}{10^{- 2}} = 1.0 \times \frac{7.64554857984}{10^{- 2}}

Cancel

x \times \frac{10^{- 2} \times 7.64554857984}{7.64554857984 \times 10^{- 2}} = 1.0 \times \frac{7.64554857984}{10^{- 2}}

Simplify

x = \frac{7.64554857984}{10^{- 2}}

Rewrite equation

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

Rewrite

x = 10^{2} \times 7.64554857984

Solve

x

x \approx 764.55485798 \approx 7.6455 \times 10^{2}

Conversion Equation

1.0 (\frac{k i l o g r a m}{c u b i c m e t e r}) \approx 7.6455 \times 10^{2} (\frac{g r a m}{c u b i c m e t e r})

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