To find 98.6% of 343.7, you can use the following formula:
\[ \text{Percentage} = \left( \frac{\text{Percentage Rate}}{100} \right) \times \text{Value} \]
Substituting the values:
\[ \text{Percentage} = \left( \frac{98.6}{100} \right) \times 343.7 \]
Calculating this:
\[ = 0.986 \times 343.7 \]
Now, performing the multiplication:
\[ 0.986 \times 343.7 = 338.6122 \]
Finally, rounding to the nearest thousandth:
\[ 338.612 \]
Thus, 98.6% of 343.7 is \(\boxed{338.612}\).