If ONLY the digit 4 in the number 847 is changed to a different digit, by how much could the number change?

Answer

To determine how much the number 847 can change by altering only the digit 4, we need to consider what happens when we change the digit 4 to any digit from 0 to 9, excluding 4 itself. Let's break down the current number: - The number is structured as hundreds, tens, and units: 800 + 40 + 7. Changing the digit 4 impacts only the tens place. Here are the possibilities for changing the digit 4: 1. Change 4 to 0: The new number = 807. Change = 807 - 847 = -40 2. Change 4 to 1: The new number = 817. Change = 817 - 847 = -30 3. Change 4 to 2: The new number = 827. Change = 827 - 847 = -20 4. Change 4 to 3: The new number = 837. Change = 837 - 847 = -10 5. Change 4 to 5: The new number = 857. Change = 857 - 847 = 10 6. Change 4 to 6: The new number = 867. Change = 867 - 847 = 20 7. Change 4 to 7: The new number = 877. Change = 877 - 847 = 30 8. Change 4 to 8: The new number = 887. Change = 887 - 847 = 40 9. Change 4 to 9: The new number = 897. Change = 897 - 847 = 50 Now we calculate the maximum change in absolute value: - The greatest positive change occurs when changing 4 to 9: 50. - The greatest negative change occurs when changing 4 to 0: -40. Thus, the maximum absolute change is 50. Therefore, the answer is C. 50.