Question

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

Answer 1

`\displaystyle 1 (gr)/(cm^3)=1,000(kg)/(m^3)`

Step-by-step 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 (gr)/(cm^3)`

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

We know that

`\displaystyle 1 gr=(1)/(1000)Kg`

`\displaystyle 1 cm^3=(1)/(1,000,000)m^3`

The conversion is

`\displaystyle 1 (gr)/(cm^3)=((1)/(1000)Kg)/((1)/(1,000,000)m^3)`

`\displaystyle 1 (gr)/(cm^3)=(1,000,000\ kg)/(1000\ m^3)=1,000(kg)/(m^3)`

Thus

`\boxed{\displaystyle 1 (gr)/(cm^3)=1,000(kg)/(m^3)}`