How is density measured in units

Mass, volume and density

Prime example

How much \ (\ frac {{\ rm {g}}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} \) are \ (10 ​​\ frac {{{\ rm {kg}}}} {{{{\ rm {m}} ^ {\ rm {3}}}}} \)? Or in short: \ (10 ​​\ frac {{{\ rm {kg}}}} {{{{\ rm {m}} ^ {\ rm {3}}}}} =? \ Frac {{\ rm {g }}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} \)

Step 1: Press the given size \ (10 ​​\ frac {{{\ rm {kg}}}} {{{{\ rm {m}} ^ {\ rm {3}}}}} \) in the desired unit \ (\ frac {{\ rm {g}}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}}} \).
\ [10 \ frac {{{\ rm {kg}}}} {{{{\ rm {m}} ^ {\ rm {3}}}}}} = 10 \ cdot \ frac {{1000 {\ rm { g}}}} {{1000000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} \]
Note: The conversion number for neighboring mass units is \ (1000 \) (\ (1 {\ rm {kg}} = 1000 {\ rm {g}} \)), the conversion number for neighboring volume units is also \ (1000 \) ( \ (1 {{\ rm {m}} ^ {\ rm {3}}} = 1000 {\ rm {d}} {{\ rm {m}} ^ {\ rm {3}}} \), \ (1 {\ rm {d}} {{\ rm {m}} ^ {\ rm {3}}} = 1000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3} }} \), so \ (1 {{\ rm {m}} ^ {\ rm {3}}} = 1000 \ cdot 1000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}} = 1000000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}} \)).

2nd step: Simplify the result.
\ [10 \ cdot \ frac {{1000 {\ rm {g}}}} {{1000000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} = 1 , 0 \ cdot \ frac {{1000 {\ rm {g}}}} {{100000 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} = 1, 0 \ cdot \ frac {{1 {\ rm {g}}}} {{100 {\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} = 1.0 \ cdot {10 ^ {- 2}} \ frac {{\ rm {g}}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} = 0.010 \ frac {{\ rm {g}}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} \]

This results in
\ [10 \ frac {{{\ rm {kg}}}} {{{{\ rm {m}} ^ {\ rm {3}}}}} = 1.0 \ cdot {10 ^ {- 2} } \ frac {{\ rm {g}}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} = 0.010 \ frac {{\ rm {g }}} {{{\ rm {c}} {{\ rm {m}} ^ {\ rm {3}}}}} \]