To calculate the approximate weight of all the ants in the world, we need two pieces of information:
- The average weight of one ant, which is given as \(3 \times 10^{-6}\) kilograms.
- The estimated number of ants in the world, which is commonly approximated to be about \(10^{18}\).
Now, we can calculate the total weight of all the ants by multiplying the average weight of one ant by the total number of ants:
\[ \text{Total Weight} = (\text{Average Weight of one ant}) \times (\text{Number of ants}) \]
Substituting in the values we have:
\[ \text{Total Weight} = (3 \times 10^{-6} \text{ kg}) \times (10^{18}) \]
To multiply these:
\[ 3 \times 10^{-6} \times 10^{18} = 3 \times 10^{(18 - 6)} = 3 \times 10^{12} \]
Thus, the approximate weight of all the ants in the world is:
\[ \boxed{3 \times 10^{12}} \text{ kilograms} \]