To find the total weight of all the ants in the world, we 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 \( 1 \times 10^{16} \).
Calculating the total weight:
\[ \text{Total weight} = (3 \times 10^{-6} , \text{kg}) \times (1 \times 10^{16}) \]
Using the properties of exponents, we can simplify this:
\[ \text{Total weight} = 3 \times 1 \times 10^{-6 + 16} = 3 \times 10^{10} \]
Thus, the approximate weight of all the ants in the world is \( \boxed{3 \times 10^{10}} \) kg.
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