The density of water is 1 g/cc. Its value in SI is

Options

A. `10^(-3)"kg"//"m"^(3)`
B. `10^(-6)"kg"//"m"^(3)`
C. `10^(3)"kg"//"m"^(3)`
D. `10^(6)"kg"//"m"^(3)`

Answer

To convert the density of water from CGS units to SI units, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Density**:
The density of water is given as 1 g/cc (grams per cubic centimeter).

2. **Understand the SI Units**:
In SI units, mass is measured in kilograms (kg) and volume is measured in cubic meters (m³). Therefore, the SI unit for density is kg/m³.

3. **Convert Mass from Grams to Kilograms**:
Since 1 gram is equal to 0.001 kilograms, we convert 1 g to kg:
\[ 1 \text{ g} = 0.001 \text{ kg} \]

4. **Convert Volume from Cubic Centimeters to Cubic Meters**:
Since 1 cubic centimeter (cc) is equal to \(10^{-6}\) cubic meters (m³), we convert cc to m³:
\[ 1 \text{ cc} = 10^{-6} \text{ m}^3 \]

5. **Calculate the Density in SI Units**:
Now we can substitute the converted values into the density formula:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{0.001 \text{ kg}}{10^{-6} \text{ m}^3} \]

6. **Perform the Calculation**:
Dividing the mass by the volume gives:
\[ \text{Density} = \frac{0.001 \text{ kg}}{10^{-6} \text{ m}^3} = 0.001 \times 10^{6} \text{ kg/m}^3 = 1000 \text{ kg/m}^3 \]

7. **Express in Scientific Notation**:
The density of water can also be expressed as:
\[ 10^{3} \text{ kg/m}^3 \]

### Final Answer:
The value of the density of water in SI units is \(10^{3} \text{ kg/m}^3\).

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