To solve this, we determine the change in the value of the number $35284$ by directly analyzing how each digit replacement alters the number's value. Let's break this into steps:

Step 1: Analyze positional values

In the number $35284$, each digit has a positional value based on its place:

• $3$ is in the ten-thousands place ($10,000$).
• $5$ is in the thousands place ($1,000$).
• $2$ is in the hundreds place ($100$).
• $8$ is in the tens place ($10$).
• $4$ is in the ones place ($1$).

Step 2: Replace digits and calculate changes

Original and New Digits:

• $3 \to 1$: Decrease of $3 - 1 = 2$, affecting the $10,000$-place.
  Change in value: $2 \times 10,000 = 20,000$ (decrease).

• $5 \to 8$: Increase of $8 - 5 = 3$, affecting the $1,000$-place.
  Change in value: $3 \times 1,000 = 3,000$ (increase).

• $8 \to 4$: Decrease of $8 - 4 = 4$, affecting the $10$-place.
  Change in value: $4 \times 10 = 40$ (decrease).

• $2$ and $4$ remain unchanged, so they have no effect on the value.

Step 3: Combine all changes

The total change in the number is the sum of the changes from each replacement: $-20,000 + 3,000 - 40 = -17,040$

Final Answer:

The change in the value of the number $35284$ is a decrease of $17,040$.

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Justification:

This reasoning approach is valid because it works directly with the positional values of the digits, avoiding subtraction algorithms. Each digit's positional impact is computed separately, ensuring accuracy.

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Would you like further clarifications or visual examples?

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Related Questions:

1. How does positional value impact the interpretation of a number?
2. What happens if you replace digits in a different order?
3. Can this method be extended to numbers with more or fewer digits?
4. What is the effect of swapping digits instead of replacing them?
5. How can this reasoning method be applied to solve problems with negative numbers?

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Tip:

Always consider the positional value when modifying digits in a number; it simplifies understanding the total effect.