To find the total weight of all the ants in the world, you can multiply the average weight of one ant by the total number of ants.
Given:
- The average weight of an ant = \(3 \times 10^{-6}\) kg
- The total number of ants = \(1 \times 10^{16}\)
Now, multiply these two quantities:
\[ \text{Total weight} = (\text{Average weight of one ant}) \times (\text{Total number of ants}) \] \[ \text{Total weight} = (3 \times 10^{-6} , \text{kg}) \times (1 \times 10^{16}) \]
When you multiply the coefficients (3 and 1) and add the exponents of 10:
\[ \text{Total weight} = 3 \times 1 \times 10^{-6 + 16} = 3 \times 10^{10} \]
Therefore, the approximate weight of all the ants in the world is:
\[ \boxed{3 \times 10^{10}} \text{ kg} \]