Question

The Density of a liquid is 1.0g/cm³. What is its density in kg/m? Show your workings clearly.​

Answer 1

Answer:

$\displaystyle 1 \frac{gr}{cm^3}=1,000\frac{kg}{m^3}$

Explanation:

Note: We are assuming the unit 'm' is 'm^3' to be compatible with the given unit.

Unit Conversions

Is the procedure followed to change the units of a certain magnitude to other units of the same magnitude. Example: centimeters to meters, hours to minutes, Kg to gr.

When dealing with composite units, each unit must be converted separately.

The density of some liquid is

$\displaystyle 1 \frac{gr}{cm^3}$

We are required to convert to $Kg/m^3$, so we convert separately

We know that

$\displaystyle 1 gr=\frac{1}{1000}Kg$

$\displaystyle 1 cm^3=\frac{1}{1,000,000}m^3$

The conversion is

$\displaystyle 1 \frac{gr}{cm^3}=\frac{\frac{1}{1000}Kg}{\frac{1}{1,000,000}m^3}$

$\displaystyle 1 \frac{gr}{cm^3}=\frac{1,000,000\ kg}{1000\ m^3}=1,000\frac{kg}{m^3}$

Thus

$\boxed{\displaystyle 1 \frac{gr}{cm^3}=1,000\frac{kg}{m^3}}$