Step 1: Recall the molar volume at STP.
At standard temperature and pressure, one mole of any ideal gas takes up the same space, namely $22.4$ litres. This is a fixed fact we can use directly.
Step 2: Find the molar mass of carbon dioxide.
Carbon has mass $12$ and each oxygen has mass $16$. So for $CO_2$: \[ 12 + 2 \times 16 = 44 \text{ g/mol} \]
Step 3: Convert the given mass into moles.
The number of moles is the given mass divided by the molar mass: \[ n = \frac{4.4}{44} = 0.1 \text{ mol} \]
Step 4: Use the molar volume to get volume.
Since each mole takes $22.4$ litres at STP, multiply the moles by this volume: \[ V = n \times 22.4 \]
Step 5: Put in the numbers.
\[ V = 0.1 \times 22.4 = 2.24 \text{ L} \]
Step 6: State the result.
So $4.4$ grams of carbon dioxide, being one tenth of a mole, occupies $2.24$ litres at STP.
\[ \boxed{2.24 \text{ L}} \]