Place value grid with numbers for educational purposes.

To solve the problem, we need to fill in the grid based on the given values and their corresponding place values. Let's break it down step by step.

Step 1: Understand the structure

The grid has four columns labeled with place values:
- 1000 (thousands place)
- 200 (hundreds place)
- 40 (tens place)
- 5 (ones place)

Each row represents a number, and the sum of the values in each column corresponds to the total value given on the right side of the grid:
- Row 1: Total = 700
- Row 2: Total = 40
- Row 3: Total = 2

Step 2: Analyze each row

We will determine the values for each cell in the grid by considering the place values and the total sums.

#### Row 1: Total = 700
- The total is 700. We need to distribute this value across the columns using the given place values (1000, 200, 40, 5).

Since 700 is less than 1000, the first column (1000) must be 0.
- Next, we check the hundreds place (200). The largest multiple of 200 that fits into 700 is 3 × 200 = 600.
- So, the second column (200) is 3.
- Remaining value: \( 700 - 600 = 100 \).

Now, we need to distribute the remaining 100 across the tens (40) and ones (5) places.
- The largest multiple of 40 that fits into 100 is 2 × 40 = 80.
- So, the third column (40) is 2.
- Remaining value: \( 100 - 80 = 20 \).

Finally, we distribute the remaining 20 across the ones place (5).
- The largest multiple of 5 that fits into 20 is 4 × 5 = 20.
- So, the fourth column (5) is 4.
- Remaining value: \( 20 - 20 = 0 \).

Thus, the values for Row 1 are:
- First column: 0
- Second column: 3
- Third column: 2
- Fourth column: 4

#### Row 2: Total = 40
- The total is 40. We need to distribute this value across the columns using the given place values (1000, 200, 40, 5).

Since 40 is less than 1000 and 200, the first two columns (1000 and 200) must be 0.
- Next, we check the tens place (40). The largest multiple of 40 that fits into 40 is 1 × 40 = 40.
- So, the third column (40) is 1.
- Remaining value: \( 40 - 40 = 0 \).

Finally, the ones place (5) must be 0 since there is no remaining value.
- So, the fourth column (5) is 0.

Thus, the values for Row 2 are:
- First column: 0
- Second column: 0
- Third column: 1
- Fourth column: 0

#### Row 3: Total = 2
- The total is 2. We need to distribute this value across the columns using the given place values (1000, 200, 40, 5).

Since 2 is less than 1000, 200, and 40, the first three columns (1000, 200, 40) must be 0.
- Finally, we check the ones place (5). The largest multiple of 5 that fits into 2 is 0 × 5 = 0.
- So, the fourth column (5) is 0.
- Remaining value: \( 2 - 0 = 2 \).

Since 2 cannot be represented using the given place values (1000, 200, 40, 5), we conclude that the ones place (5) must be 0, and the remaining value is not representable with the given place values. However, if we assume the problem allows for a remainder or an error, we can still fill in the grid as best as possible.

Thus, the values for Row 3 are:
- First column: 0
- Second column: 0
- Third column: 0
- Fourth column: 0

Step 3: Fill in the grid

Based on the calculations above, the completed grid is:

| 1000 | 200 | 40 | 5 |
|------|-----|----|---|
| 0 | 3 | 2 | 4 |
| 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
0 & 3 & 2 & 4 \\
\hline
0 & 0 & 1 & 0 \\
\hline
0 & 0 & 0 & 0 \\
\hline
\end{array}
}
\]