Calculate the Sum: 0.96 + 0.58 Using Vertical Addition

To solve this problem, we will add the decimals $0.96$ and $0.58$ following these detailed steps:

Step 1: Align the numbers by their decimal points:

$\begin{aligned} \phantom{+} 0&.96 \\ + 0&.58 \\ \underline{\phantom{7765}}& \underline{\phantom{7745}} \\ \end{aligned}$

Step 2: Add the rightmost column (hundredths place).

$6 + 8 = 14$

Write 4 in the hundredths place and carry over 1 to the tenths place.

Step 3: Add the tenths column including the carry-over.

$9 + 5 + 1 = 15$

Write 5 in the tenths place and carry over 1 to the units place.

Step 4: Add the units (whole number) column including the carry-over.

$0 + 0 + 1 = 1$

Write 1 in the units place.

Result: Write down the final sum.

Therefore, the sum is $\mathbf{1.54}$.