Four and Five Digit Numbers and their Formation | ORCHIDS
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Numbers

Four-digit Numbers

  • The numbers having 4-digits are called the 4-digit numbers, provided its starting digit is not 0. For example:
  • 3426, 3570, 1023, 0213

    0213 is not a 4-digit number because it starts with 0.

  • Four-digit numbers begin with 1000, read as ‘one thousand’.
  • The smallest 4-digit number is 1000 (one thousand).
  • The greatest 4-digit number is 9999 (nine thousand nine hundred ninety-nine).
  • There are 9000 four-digit numbers in all.
  • The greatest 3-digit number is 999. When we add 1 to 999, we get the smallest four-digit number.
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Predecessor:

Predecessor of a number is the number that precedes or comes before the number. To find the predecessor of a number subtract 1 from it.

Successor:

Successor of a number is the number that succeeds or comes after the number. To find the successor of a number, add 1 to it.

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Five-digit Numbers

  • The numbers having 5-digits are called the 5-digit numbers, provided its starting digit is not 0. For example:
  • 31426, 30570, 10023, 03213

    03213 is not a 5-digit number because it starts with 0.

  • Five-digit numbers begin with 10000, read as ‘ten thousand’.
  • The smallest 5-digit number is 10000 (ten thousand).
  • The greatest 5-digit number is 99999 (ninety-nine thousand nine hundred ninety-nine).
  • There are 90000 five-digit numbers in all.
  • The greatest 4-digit number is 9999. When we add 1 to 9999, we get the smallest five-digit number.
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Forming Numbers

If some digits are given, we can form the greatest and smallest possible numbers by rearranging the given digits.

Without repeating the digits:

  • To form the greatest possible number, arrange the digits in the descending order.
  • To form the smallest possible number, arrange the digits in the ascending order. If the given digits have 0, then start with the second smallest digit and use 0 in the second place.

Example:

Form the smallest and the greatest possible 4-digits numbers using the digits 5, 7, 2, and 0.

Answer

Step 1: First arrange the digits in the ascending order to get the smallest number.

0, 2, 5, 7

Since there is a 0, start with the second smallest number, that is 2, and place the 0 at the second place.

Therefore, the smallest possible number is 2057.

Step 2: Arrange the digits in the descending order to get the largest possible number.

7, 5, 2, 0

Therefore, the largest possible number is 7520.

With repeating the digits:

  • To form the greatest possible number, arrange the digits in the descending order and repeat the largest digits as many times as required.
  • To form the smallest number, arrange the digits in the ascending order and repeat the smallest digits as many times as required. If the given digits have 0, then start with the second smallest digit and use 0 in the second place.

Example:

Frame the smallest and the greatest possible 4-digits numbers using the digits 3, 6, 0.

Answer

Step 1: To get the 4-digit number, one digit has to be repeated. Arrange the digits in the ascending order.

0, 3, 6

The smallest digit is 0. Therefore, 0 will be repeated.

The smallest possible number is 3006.

Step 2: Arrange the digits in the descending order.

6, 3, 0

The largest digit is 6. Therefore, 6 will be repeated.

The greatest possible number is 6630.

Fun facts:

  • One hundred is 10 times 10
  • One thousand is 10 times 100
  • Ten thousand is 10 times 1000

Did you know?

ATM cards have a unique Personal Identification Number (PIN). Generally, a PIN is a 4-digit code. You can make 10000 different 4-digit codes using the digits 0 to 9.

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