Comparing and Ordering of Numbers

Condition 1: Numbers having different number of digits

The numbers having less number of digits are always smaller than the numbers having more number of digits

Example

54,000 < 1,58,000

2,78,900 > 56,000

Condition 2: Numbers having same number of digits

If both the numbers have the same numbers of digits, then we comparing the digits from the extreme left to find the first place where they differ.

Example 1: Compare 42567 and 55567

First compare the digits in ten thousands place.

Here digits differ, 4 and 5 are in ten thousands place and 5 > 4. Hence 42567 < 55567

Example 2: Compare 14467 and 15567

Both numbers have the same digit in ten thousands place. Hence we compare the digits in thousands place.

4 and 5 are in thousands place and 5 > 4. Hence 14467 < 15567

Example 3: Compare 14467 and 14457

Numbers have same digit in ten thousands, thousands and hundreds place. Hence we compare the digits in tens place.

6 and 5 are in the tens place and 6 > 5. Hence 14467 > 14457

Example 4: Compare 14457 and 14452

Numbers have same digit in ten thousands, thousands, hundreds and tens place. Hence we compare the digits in ones place.

7 and 2 are in the ones place and 7 > 2. Hence 14457 >14452.

Example 5: Compare 14567 and 14567

Both numbers have the same digits in all the places. Hence, both numbers are equal.

Ordering of numbers

Ascending Orders / Increasing Orders

Arranging the numbers from smallest to the greatest is known as increasing order or ascending order.

Descending Orders / Decreasing Orders

Arranging the numbers from greatest to the smallest is known as decreasing order or descending order.

Example 1: Arrange the following numbers in the ascending and descending orders.

61478, 50478, 65790, 94090

Ascending Orders

Writing from the smallest number to the greatest number

50478 < 61478 < 65790 < 94090

Descending Orders

Writing from greatest number to the smallest number

94090 > 65790 > 61478 > 50478