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.
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Here are the solutions for questions 8, 9, and 10: 8. Given digits: 4, 7, and 9. a) Write the possible numbers of three-digits formed from the given digits. Step 1: List all permutations of the digits 4, 7, and 9. The possible three-digit numbers are: • 479 • 497 • 749 • 794 • 947 • 974 The possible three-digit numbers are 479, 497, 749, 794, 947, 974. b) What are the smallest and the greatest number among these three-digit numbers? Step 1: Identify the smallest number from the list. The smallest number is formed by arranging the digits in increasing order: 479. Step 2: Identify the greatest number from the list. The greatest number is formed by arranging the digits in decreasing order: 974. The smallest number is 479 and the greatest number is 974. 9. Given digits: 3, 0, 8, and 6. a) Write the four-digit number by arranging the given digits in decreasing order. Step 1: Arrange the digits 3, 0, 8, 6 in decreasing order. The digits in decreasing order are 8, 6, 3, 0. The four-digit number is 8630. b) Write a four-digit number by arranging the given digits in increasing order. Step 1: Arrange the digits 3, 0, 8, 6 in increasing order. The digits in increasing order are 0, 3, 6, 8. Step 2: Form a four-digit number. Since 0 cannot be the first digit, place the smallest non-zero digit first, followed by 0, then the remaining digits in increasing order. The four-digit number is 3068. c) Write the smallest and the greatest numbers of four-digit formed by these digits. Step 1: Determine the smallest four-digit number. Using the digits 3, 0, 8, 6, the smallest four-digit number is formed by placing the smallest non-zero digit first, then 0, then the rest in increasing order: 3068. Step 2: Determine the greatest four-digit number. Using the digits 3, 0, 8, 6, the greatest four-digit number is formed by arranging the digits in decreasing order: 8630. The smallest four-digit number is 3068 and the greatest four-digit number is 8630. 10. a) Find the sum of the greatest and the least numbers of 6 digits. Step 1: Identify the greatest 6-digit number. The greatest 6-digit number is 999,999. Step 2: Identify the least 6-digit number. The least 6-digit number is 100,000. Step 3: Calculate their sum. 999,999 + 100,000 = 1,099,999 The sum is 1,099,999. b) Find the difference between the greatest and the least numbers of 7-digits formed by 3, 0, 1, 8, 5, 9, 4. Step 1: List the given digits in order: 0, 1, 3, 4, 5, 8, 9. Step 2: Form the greatest 7-digit number using these digits. Arrange the digits in decreasing order: 9854310. Step 3: Form the least 7-digit number using these digits. Arrange the digits in increasing order, with the smallest non-zero digit first: 1034589. Step 4: Calculate the difference between the greatest and the least numbers. 9,854,310 - 1,034,589 = 8,819,721 The difference is 8,819,721. That's 2 down. 3 left today — send the next one.