To find the approximate weight of all the ants in the world, you can multiply the average weight of an ant by the total number of ants:
\[ \text{Total Weight} = (\text{Weight of one ant}) \times (\text{Number of ants}) \]
Given:
- Weight of one ant = \(3 \times 10^{-6}\) kg
- Number of ants = \(1 \times 10^{16}\)
Now, substituting the values:
\[ \text{Total Weight} = (3 \times 10^{-6} , \text{kg}) \times (1 \times 10^{16}) \]
Using the properties of exponents, we can multiply:
\[ = 3 \times 1 \times 10^{-6 + 16} \] \[ = 3 \times 10^{10} \]
Therefore, the approximate weight of all the ants in the world is:
\[ \boxed{3 \times 10^{10}} \text{ kg} \]