Question

The density of balsa wood is about $170kg/{m^3}$ . How do you convert it to $g/c{m^3}$ ?

Answer 1

Hint : To convert the given expression, first we will change the $kg$ into $g$ by multiplying with ${10^3}g$ and again convert the ${m^3}$ into $c{m^3}$ by multiplying with ${10^{ - 3}}m$ separately. And that’s how we will convert the given expression into its shortest unit forms.

Complete Step By Step Answer:
We need to use two conversion factors, one to take us from kilograms to grams and one to take us from $cubic{\text{ }}meters$ to $cubic{\text{ }}centimeters$ .
As we know that, $1kg$ is equivalent to $10^3$ g . This means that in order to convert from $kilograms$ to $grams$ . We need to multiply whatever value we have by ${10^3}$ .
Let’s convert kilograms per $cubic{\text{ }}meter$ to $grams{\text{ }}per{\text{ }}cubic{\text{ }}meter$ .
$170\dfrac{{kg}}{{{m^3}}}.\dfrac{{{{10}^3}g}}{{1kg}} = {170.10^3}g/{m^3}$
Now focus on the volume. First, we have that $1{m^3}$ is equivalent to
$1{m^3} = 1m \times 1m \times 1m$
Similarly, $1c{m^3}$ will be equivalent to
$1c{m^3} = 1cm \times 1cm \times 1cm$
And, $1cm = \dfrac{1}{{{{10}^2}}}m = {10^{ - 2}}m$
Therefore, 1 $cm^3$ will be
$1c{m^3} = {10^{ - 2}}m \times {10^{ - 2}}m \times {10^{ - 2}}m = {10^{ - 6}}{m^3}$
That’s how we can convert the density from $grams{\text{ }}per{\text{ }}cubic{\text{ }}meter$ to $grams{\text{ }}per{\text{ }}cubic{\text{ }}centimetre$ .
${170.10^3}\dfrac{g}{{{m^3}}}.\dfrac{{{{10}^{ - 6}}{m^3}}}{{1c{m^3}}} = 0.17g/c{m^3}$
Hence, the conversion of $170 kg/m^3$ is $0.17g/c{m^3}$ .

Note :
Generally, the conversion of one unit to another unit of the same quantity is performed using multiplicative conversion factors. Let’s see how to convert a different unit of length and mass. The conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.