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, 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?

---

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.

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.

Explore how Sienna can rearrange the digits in 1,258,072 to satisfy the condition where one digit is 10 times the value of another. This solution breaks down number theory concepts, explores multiplicative relationships, and offers a step-by-step rearrangement to form the number 8752210. Suitable for Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation