Let's analyze the statements provided, focusing on the values of the specified digits in both numbers:
-
For the digit 7 in 1,725:
- The digit 7 is in the hundreds place, which means its value is \(7 \times 100 = 700\).
For the digit 7 in 5,712:
- The digit 7 is in the tens place, which means its value is \(7 \times 10 = 70\).
- Comparing the two, \(700\) is \(10\) times \(70\), so statement A is true.
-
For the digit 2 in 1,725:
- The digit 2 is in the tens place, giving it a value of \(2 \times 10 = 20\).
For the digit 2 in 5,712:
- The digit 2 is in the units place, giving it a value of \(2 \times 1 = 2\).
- Comparing the two, \(20\) is \(10\) times \(2\), so statement B is also true.
-
For the digit 1 in 1,725:
- The digit 1 is in the thousands place, giving it a value of \(1 \times 1000 = 1000\).
For the digit 1 in 5,712:
- The digit 1 is in the hundreds place, which means its value is \(1 \times 100 = 100\).
- Comparing the two, \(1000\) is \(10\) times \(100\), making statement C true.
-
For the digit 2 in 5,712:
- The digit 2 is in the units place, giving it a value of \(2 \times 1 = 2\).
For the digit 2 in 1,725:
- The digit 2 is in the tens place, giving it a value of \(2 \times 10 = 20\).
- Here we see \(2\) is not \(10\) times \(20\), thus statement D is false.
Conclusion: The correct statements are A, B, and C. A specific answer to your query based on the choices initially listed would render A. The value of the digit 7 in 1,725 is 10 times greater than the value of the digit 7 in 5,712 as true, but all three initial options (A, B, and C) contain valid truths.