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A) Find the sum of the greatest and the least numbers of 6 digits. b) Find the difference between the greatest and the least numbers formed by 7-digits: 3, 0, 1, 8, 5, 9, 4.

Mathematics

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10. a) Find the sum of the greatest and the least numbers of 6 digits.

  1. Identify the greatest 6-digit number.

    The greatest 6-digit number is 999,999.

  2. Identify the least 6-digit number.

    The least 6-digit number is 100,000.

  3. Calculate their sum.

    999,999+100,000=1,099,999999,999 + 100,000 = 1,099,999

    The sum of the greatest and the least 6-digit numbers is 1,099,999\boxed{1,099,999}.

    10. b) Find the difference between the greatest and the least numbers formed by 7-digits: 3, 0, 1, 8, 5, 9, 4.

  4. Identify the given digits.

    The given digits are $3, 0, 1, 8, 5, 9, 4$.

  5. Form the greatest 7-digit number using these digits.

    To form the greatest number, arrange the digits in descending order: $9, 8, 5, 4, 3, 1, 0$.
    The greatest 7-digit number is 9,854,310.

  6. Form the least 7-digit number using these digits.

    To form the least number, arrange the digits in ascending order, ensuring the first digit is not zero. The smallest non-zero digit is 1.
    So, arrange as: $1, 0, 3, 4, 5, 8, 9$.
    The least 7-digit number is 1,034,589.

  7. Calculate the difference between the greatest and the least numbers.

    9,854,310−1,034,589=8,819,7219,854,310 - 1,034,589 = 8,819,721

    The difference between the greatest and the least numbers formed by the given digits is 8,819,721\boxed{8,819,721}.

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