To find the total thickness of a stack of 98 sheets of metal, each of which is 1/3 of an inch thick, we can multiply the thickness of one sheet by the number of sheets:
\[ \text{Total thickness} = \text{Thickness of one sheet} \times \text{Number of sheets} \]
Substituting the values:
\[ \text{Total thickness} = \frac{1}{3} \times 98 \]
To perform the multiplication, we can express 98 as a fraction:
\[ 98 = \frac{98}{1} \]
Now, we multiply the fractions:
\[ \text{Total thickness} = \frac{1 \times 98}{3 \times 1} = \frac{98}{3} \]
Now, we can convert \(\frac{98}{3}\) into a mixed number. We divide 98 by 3:
\[ 98 \div 3 = 32 \quad \text{(with a remainder of 2)} \]
This gives us:
\[ 98 = 3 \times 32 + 2 \]
Thus, as a mixed number, we have:
\[ \frac{98}{3} = 32 \frac{2}{3} \]
Therefore, the total thickness of the stack of sheets is:
\[ \boxed{\frac{98}{3}} \quad \text{or} \quad \boxed{32 \frac{2}{3}} \]