This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the difference between the greatest and smallest numbers formed by the digits 7, 2, 0, and 5, using each digit only once, we follow these steps: Step 1: Form the greatest number. To form the greatest number, arrange the given digits in descending order. The digits are 7, 2, 0, 5. Arranging them in descending order gives: 7, 5, 2, 0. The greatest number is 7520 Step 2: Form the smallest number. To form the smallest number, arrange the given digits in ascending order. However, a number cannot start with zero if it is a four-digit number. Therefore, place the smallest non-zero digit first, followed by zero, and then the remaining digits in ascending order. The digits are 7, 2, 0, 5. The smallest non-zero digit is 2. Arranging them to form the smallest number gives: 2, 0, 5, 7. The smallest number is 2057 Step 3: Calculate the difference between the greatest and smallest numbers. Subtract the smallest number from the greatest number. 7520 - 2057 7520 - 2057 = 5463 The difference between the greatest and smallest numbers is 5463. Drop the next question 📸