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.
The average weight of an ant is \(3 \times 10^{-6}\) kg, and the total number of ants is \(1 \times 10^{16}\).
So, the total weight \(W\) can be calculated as follows:
\[ W = (3 \times 10^{-6} , \text{kg}) \times (1 \times 10^{16}) \]
Now perform the multiplication:
\[ W = 3 \times 1 \times 10^{-6} \times 10^{16} = 3 \times 10^{10} , \text{kg} \]
Thus, the approximate weight of all the ants in the world is
\[ \boxed{3 \times 10^{10}} , \text{kg}. \]
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