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Let's solve the problem step by step:

We need to arrange the digit cards \( 0, 1, 4, 5, 6, 8 \) to create numbers that round to the specified values.

### a) 500,000 to the nearest 100,000
To round to 500,000 to the nearest 100,000, the number should be between 450,000 and 549,999. Let's find a combination:

- One possibility is \( 514,000 \), as it rounds to 500,000.

### b) 610,000 to the nearest 10,000
To round to 610,000 to the nearest 10,000, the number should be between 605,000 and 614,999. Let's find a combination:

- One possibility is \( 610,458 \), as it rounds to 610,000.

### c) 611,000 to the nearest 1,000
To round to 611,000 to the nearest 1,000, the number should be between 610,500 and 611,499. Let's find a combination:

- One possibility is \( 611,458 \), as it rounds to 611,000.

Now, let's summarize the solutions:

1. \( 514,000 \) rounds to 500,000.
2. \( 610,458 \) rounds to 610,000.
3. \( 611,458 \) rounds to 611,000.

Would you like more details on how these numbers were chosen, or do you have any questions? Here are five related questions to expand your understanding:

1. How do you determine the range of numbers that round to a specific value?
2. What other combinations of the given digits could also round to 500,000?
3. Can you explain the process of rounding a number to the nearest thousand?
4. How would the solution change if we had to round to the nearest ten?
5. What are some real-life applications of rounding numbers?

**Tip:** When rounding numbers, always identify the range that would round to your target value to help in finding possible combinations.

Arrange the digit cards (0, 1, 4, 5, 6, 8) to make a number that rounds to:
a) 500,000 to the nearest 100,000
b) 610,000 to the nearest 10,000
c) 611,000 to the nearest 1,000

Solve the problem of arranging digit cards (0, 1, 4, 5, 6, 8) to create numbers that round to 500,000, 610,000, and 611,000. Learn key concepts in place value and rounding for grades 4-6.

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