# Comparison of Four-digit Numbers

What are the rules for the comparison of four-digit numbers?

We have already learnt that a two-digit number is always greater than a single digit number. But, in case of comparison of four-digit numbers, we must consider the following facts:

(i) The number having more digits is greater i.e., a four-digit number is always greater than a three-digit number, two-digit number or one-digit number separately. As:

1000 > 999 , 1000 > 798 , 1000 > 191 ,

3275 > 375 , 5823 > 823 , 4378 > 937 , etc.

(ii) In case of two four-digit numbers, the digits on the extreme left, i.e., Thousand-place digit or 4th digit from the right are compared.

(a) The number having the greater extreme left digit, is the greater number.

5738 > 3561 , 9721 > 8925 , 2193 > 1293 as 5 > 3, 9 > 8, etc.

(b) If the digits on the extreme left are equal, then the rules to compare three-digit numbers are followed, as:

(i) 5738 > 5698 , 9794 > 9695 , 1548 > 1499

(ii) 5738 > 5729 , 9794 > 9784 , 1548 > 1529

(iii) 1968 > 1965 , 9798 > 9796 , 1548 > 1532

In general we can form the following rules to compare two or more numbers:

(a) If two numbers have equal number of digits, the number having greater valued digit on the extreme left is greater.

(b) If the digits on extreme left of the numbers are equal then the digits to the right of the extreme left digits are compared and so on.

How to arrange 4-digit numbers in ascending and descending order:

(i) Arranging the numbers 2137, 1815, 3279, 4716, 3373 in ascending order:

The numbers are arranged in ascending order 1815, 2137, 3279, 3373, 4716.

(ii) Arranging the numbers 5204, 3418, 7432, 5855, 2195 in descending order:

The numbers are arranged in descending order 7432, 5855, 5204, 3418, 2195.

(iii) Arranging the numbers 6001, 3145, 1111, 2157, 4679 in ascending order:

The numbers are arranged in ascending order 1111, 2157, 3145, 4679, 6001.

(iv) Arranging the numbers 3004, 3098, 3382, 3531, 3461 in descending order:

The numbers are arranged in descending order 3531, 3461, 3382, 3098, 3004.

Thus, any five-digit number is always greater than a four-digit number and so on...

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