To solve this, we need to rearrange the digits of 1,258,072 such that the value of one digit becomes 10 times the value of another digit.

Step 1: List the digits of the number

The digits in 1,258,072 are: $1, 2, 5, 8, 0, 7, 2$

Step 2: Identify pairs where one digit is 10 times another

We are looking for pairs of digits where the value of one digit is 10 times the value of another digit.

The digit 1 can be 10 times 0 because: $1 = 10 \times 0$

No other digits satisfy this condition.

Step 3: Rearrange the digits

To satisfy the condition, we can rearrange the digits in any order, keeping the numbers 1 and 0 in the number. One possible rearrangement of the digits is: $8, 7, 5, 2, 2, 1, 0$

Thus, a number Sienna could write is 8752210.

Step 4: Justification

In the number 8752210, the digit 1 is 10 times the value of the digit 0, which satisfies the condition.

Would you like more details or have any questions?

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Here are 5 related questions:

1. How many different numbers can be formed by rearranging the digits of 1,258,072?
2. What is the largest possible number that can be formed using the digits of 1,258,072?
3. How does the concept of multiples apply when rearranging digits of a number?
4. Can you find a number where two different digits have a 10-to-1 ratio, besides 1 and 0?
5. How does the inclusion of zero affect number rearrangements?

Tip: When rearranging digits, always consider how special properties (like multiples) apply to the set of available digits.