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.