How to form numbers with digits?
We know that all the numbers are formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0. Some numbers are formed with one digit, some with two digits and some with many digits.
(i) There are 9 numbers of one digit. The smallest one-digit number is 1 (one) and greatest one-digit number is 9. All the digits become numbers when used as a number.
(ii) There are 90 numbers of two digits. The smallest two-digit number is 10 and greatest two-digit number is 99. In a two-digit number, one digit is placed at ten’s place and the other at one’s place.
Given only two digits, we can form only two different two-digit numbers.
(a) Let the given digits be 4 and 9.
The two numbers that may be formed are 49 and 94.
The greater number is 94 and the smaller number is 49.
(b) Similarly, let the given digits be 7 and 2.
The two numbers that may be formed are 72 and 27.
Here, 27 is the smaller number and 72 is the greater number.
(iii) There are 900 numbers having three digits.
The smallest three-digit numbers is 100 and the greatest three-digit number is 999.
Given 3 digits, we can form 6 three-digit numbers.
(a) Let the given digits be 2, 5 and 6.
In forming the numbers with digits we may put the digits 2, 5 and 6 at Hundred-place, Tens-place and Ones-place turn by turn and get the different numbers, as: 256, 526, 625, 265, 562, 652.
The greatest number is 652 and the smallest number is 256.
(b) Similarly, let the given digits be 3, 0, 7
The numbers formed are 307, 703, 370, 730.
Two others are 037 and 073 but these are equivalent to 37 and 73 and these are two-digit numbers.
So, the three-digit numbers are 307, 703, 370 and 730in which 730 is the greatest number and 307 is the smallest number.
(iv) Similarly to form numbers with digits, like four-digit numbers.
(a) Let the given digits be 2, 3, 5, 7
The numbers (four-digit numbers) are 2357, 2573, 2735, 3257, 3527, 3725, 5723, 5237, 5327, 7532, 7325, etc.
The greatest four-digit number is 7532 and smallest four-digit number is 2357.
● To get the smallest number, we write the smallest digit at the extreme left, then the digits are placed to the right of it in increasing order till we get a four-digit number. As in the above example, 2357 is the smallest number.
● To get the greatest number, we write the greatest digit at the extreme left, then the digits are placed to its right in decreasing order till we get a four-digit number. As in the above example, 7532 is the greatest number.
● If there is 0 among the given digits, it is not written at the extreme left. If 5, 0, 3, 7 are the given digits, the smallest number is 3057 and the greatest number is 7530.
To form numbers with digits we can consider 0357, 0375, etc., as four-digit numbers.
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