Question 160329
convert {{{17.2}}}{{{g/cm^3}}} to {{{kg/m^3}}}
<pre><font size = 4 color = "indigo"><b>
Begin with

{{{17.2g/cm^3}}}

then write the {{{cm^3}}} as {{{cm*cm*cm}}}

{{{(17.2g)/(cm*cm*cm)}}}

Now we know that {{{1000g=1kg}}}, so we make a
unit fraction (one that equals 1) from that. We
will put the {{{1000g}}} in the denominator so
it will cancel with the {{{g}}} in the numerator.
So we will multiply by {{{1kg/(1000g)}}}

{{{(17.2g)/(cm*cm*cm)}}}×{{{1kg/(1000g)}}}

and, as you see, the grams {{{g}}}'s cancel out:

{{{(17.2cross(g))/(cm*cm*cm)}}}×{{{1kg/(1000cross(g))}}}

Now we know that {{{100cm=1m}}}, so we make a
unit fraction (one that equals 1) from that. We
will put the {{{100cm}}} in the numerator so
it will cancel with the {{{cm}}} in the denominator.
So we will multiply by {{{100cm/(1m)}}}.
However since there are three factors of {{{cm}}},
we will multiply it three times:

{{{(17.2cross(g))/(cm*cm*cm)}}}×{{{1kg/(1000cross(g))}}}×{{{100cm/(1m)}}}×{{{100cm/(1m)}}}×{{{100cm/(1m)}}}

Now you see that the {{{cm}}}'s all cancel out

{{{(17.2cross(g))/(cross(cm)*cross(cm)*cross(cm))}}}×{{{1kg/(1000cross(g))}}}×{{{100cross(cm)/(1m)}}}×{{{100cross(cm)/(1m)}}}×{{{100cross(cm)/(1m)}}}

{{{(17.2(1kg)(100)(100)(100))/(1000*1m*1m*1m)}}}

{{{(17200000kg)/(1000m*m*m)}}}

{{{(17200cross(000)kg)/(1cross(000)m*m*m)}}}

{{{(17200kg)/(1m*m*m)}}}

{{{(17200kg)/(1m^3)}}}

{{{17200}}}{{{kg/m^3}}}

Edwin</pre>