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 can change by altering only the digit '4' in '847', we first need to identify the current contribution of the digit '4' to the overall number. The number 847 can be broken down as follows: - 8 is in the hundreds place, contributing 800 to the number. - 4 is in the tens place, contributing 40 to the number. - 7 is in the units place, contributing 7 to the number. Thus, the number can be expressed as: 847 = 800 + 40 + 7. Now, we will consider changing the digit '4', which is in the tens place (40), to another digit (from 0 to 9, excluding 4 itself). The other digits remain the same (8 and 7). 1. If we change '4' to '0', the new number will be: - 800 + 0 + 7 = 807. - The change from 847 to 807 will be: - 847 - 807 = 40. 2. If we change '4' to '1', the new number will be: - 800 + 10 + 7 = 817. - The change will be: - 847 - 817 = 30. 3. If we change '4' to '2', the new number will be: - 800 + 20 + 7 = 827. - The change will be: - 847 - 827 = 20. 4. If we change '4' to '3', the new number will be: - 800 + 30 + 7 = 837. - The change will be: - 847 - 837 = 10. 5. If we change '4' to '5', the new number will be: - 800 + 50 + 7 = 857. - The change will be: - 857 - 847 = 10. 6. If we change '4' to '6', the new number will be: - 800 + 60 + 7 = 867. - The change will be: - 867 - 847 = 20. 7. If we change '4' to '7', the new number will be: - 800 + 70 + 7 = 877. - The change will be: - 877 - 847 = 30. 8. If we change '4' to '8', the new number will be: - 800 + 80 + 7 = 887. - The change will be: - 887 - 847 = 40. 9. If we change '4' to '9', the new number will be: - 800 + 90 + 7 = 897. - The change will be: - 897 - 847 = 50. The greatest change occurs when we convert '4' to '0', resulting in a change of 40 (847 to 807) or from '4' to '9', which results in a change of 50 (847 to 897). Therefore, the total possible changes are: - Changing to 0 results in a difference of 40. - Changing to 1 results in a difference of 30. - Changing to 2 results in a difference of 20. - Changing to 3 results in a difference of 10. - Changing to 5 results in 10, and so on. By changing '4' to either '0' or '9', the maximum change in the number 847 is **50**.