Sienna wants to rearrange the digits in the number 1,258,072 so that the value of one of the digits is 10 times the value of another digit in her number. What number could she write? Justify your answer.

To solve this problem, we need to identify if it's possible to rearrange the digits of the number **1,258,072** such that one of the digits is 10 times the value of another digit.

### Step 1: List the digits of the number
The digits of the number 1,258,072 are:  
1, 2, 5, 8, 0, 7, 2

### Step 2: Identify relationships where one digit is 10 times another
We need to look for pairs of digits where the value of one digit is 10 times another digit. Let's evaluate the digits:
- 1 × 10 = 10 (This is not a single digit, so it doesn't work.)
- 2 × 10 = 20 (Again, not a single digit.)
- 5 × 10 = 50 (Not a single digit.)
- 8 × 10 = 80 (Not a single digit.)
- 0 × 10 = 0 (This doesn’t help.)

However, the digit **1** is **10 times the digit 0**, which is the key relationship we are looking for.

### Step 3: Rearrange the digits to maintain this relationship
We can rearrange the digits in any order. For example, a possible arrangement could be:

**1, 2, 5, 0, 8, 7, 2**

In this arrangement, the digit **1** is 10 times the digit **0**, so the condition is satisfied.

### Conclusion:
One possible number Sienna could write is **1,250,872**. This number maintains the condition that the digit 1 is 10 times the digit 0.

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Would you like more details or have any questions? Here are five related questions:

1. Could there be more than one valid rearrangement of the digits?
2. How many total different numbers can be formed by rearranging the digits of 1,258,072?
3. How does the presence of a zero affect the rearrangements of the digits?
4. Can you have a similar relationship in other base systems, like base 8 or base 16?
5. Is it possible for a number to have multiple digit pairs where one is 10 times another?

**Tip:** When rearranging digits, always consider the significance of zero, as it can't be the leading digit in most cases.

Explore how Sienna can rearrange the digits of 1,258,072 to satisfy the condition where one digit is 10 times the value of another. This problem focuses on number theory and digit relationships, making it suitable for students in Grades 5-7.

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