The density of alcohol is `0.8 g cm^(-3)` . In S.I. unit, it will be :

Options

A. `0.8 kg m^(-3)`
B. `0.0008 kg m^(-3)`
C. `800 kg m^(-3)`
D. `8 xx 10^3 kg m^(-3)`

Answer

To convert the density of alcohol from grams per cubic centimeter to kilograms per cubic meter, we can follow these steps:

### Step 1: Understand the given density
The density of alcohol is given as:
\[ \text{Density} = 0.8 \, \text{g/cm}^3 \]

### Step 2: Convert grams to kilograms
We know that:
\[ 1 \, \text{g} = 0.001 \, \text{kg} \]
So, to convert grams to kilograms, we can use the conversion factor:
\[ 0.8 \, \text{g} = 0.8 \times 0.001 \, \text{kg} = 0.0008 \, \text{kg} \]

### Step 3: Convert cubic centimeters to cubic meters
We also know that:
\[ 1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3 \]
Thus, to convert cubic centimeters to cubic meters, we multiply by \( 10^{6} \):
\[ 1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3 \]

### Step 4: Combine the conversions
Now we can express the density in SI units (kg/m³):
\[ \text{Density} = \frac{0.8 \, \text{g}}{1 \, \text{cm}^3} = \frac{0.8 \times 0.001 \, \text{kg}}{10^{-6} \, \text{m}^3} \]
This simplifies to:
\[ \text{Density} = \frac{0.0008 \, \text{kg}}{10^{-6} \, \text{m}^3} = 0.0008 \times 10^{6} \, \text{kg/m}^3 = 800 \, \text{kg/m}^3 \]

### Step 5: Conclusion
Thus, the density of alcohol in SI units is:
\[ \text{Density} = 800 \, \text{kg/m}^3 \]

### Final Answer:
The correct option is 800 kg/m³.

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