Add Three-Digit Numbers: Solving 822 + 178

To solve this problem, we'll follow these steps:

• Step 1: Align the numbers vertically by their place values.
  The numbers are given as:

$\begin{aligned} &822 \\ + &178 \\ \end{aligned}$

• Step 2: Add the digits from right to left, starting with the units place.

Units place addition:
$2 + 8 = 10$

We place $0$ in the units place and carry over $1$ to the tens place.

• Step 3: Add the digits in the tens place, including the carry-over.

$2 + 7 = 9$, plus the carried over $1$:
$9 + 1 = 10$

We place $0$ in the tens place and carry over $1$ to the hundreds place.

• Step 4: Add the digits in the hundreds place, including the carry-over.

$8 + 1 = 9$, plus the carried over $1$:
$9 + 1 = 10$

Place $0$ in the hundreds place and carry over $1$ to the next place, creating a new thousands place digit.

Resulting sum:

$\begin{aligned} &1000 \end{aligned}$

Therefore, the solution to the problem is $1000$.