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The number of elements of 7.2 formed by the digits 0 and 5.

Mathematics

ScanSolve AI Answer

Answer

5463\text{5463}

Step-by-step solution

3 steps

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:

  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 75207520

  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 20572057

  3. Calculate the difference between the greatest and smallest numbers.

    Subtract the smallest number from the greatest number.

    7520−20577520 - 2057 7520−2057=54637520 - 2057 = 5463

    The difference between the greatest and smallest numbers is 5463\text{5463}.

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