**Comparing and Ordering Numbers**

**Comparing Numbers**

When working with the numbers, it's important to be able to compare the value of two or more numbers and arrange them in order. The process to find if a number is greater than, smaller than or equal to the other number is called comparison of numbers.

**Symbols used to Compare Numbers:**

**How to compare numbers**

Rules |
Example |

1) If the two numbers have different number of digits, then the number with more digit is the greater one. | 12645 > 1264 Since 12645 is 5 digit number and 1264 is 4 digit number |

2)If the numbers have same number of digits, then the number which is ahead in counting is the greater one. | 3856 > 3855 As 3855 + 1 = 3856 |

3)If the numbers have same digit, then one should start comparing from the thousand places. | 9876 > 8976 Since 9 > 8 |

4)If the thousand place digits are same then one should start comparing from the hundred place and the rest of the process will be going same. | 4823 > 4756 Since 8 > 7 |

5)If the hundred place digits are same then one should start comparing from the 10th place. | 3697 > 3684 |

6)If the 10th place digits are same then one should start comparing from the oneâ€™s place. | 2543 < 2544 |

**Ordering Numbers**

The process of arranging given numbers either in increasing order (ascending order) or in decreasing order (descending order) is called ordering of number.

**Arranging in ascending order:**

- Compare all the given numbers with the smallest number should be the 1st number when arranging in ascending order.
- Continue the same process for the rest of the given numbers.

**Example: **

Arrange the given numbers in the ascending order 2564, 2478, 3596.

**Answer: **

Comparing the numbers at thousandâ€™s place, it is clear that

3 > 2. So, the smallest number among these numbers is one of 2564 and 2478.

The smallest number between 2564 and 2478 is 2478, as 5, and 4 are digits at hundredâ€™s place and 5 > 4.

So, 2478 < 2564 < 3596.

Hence, the ascending order for the numbers will be 2478, 2564, 3596.

**Arranging in descending order:**

- After comparing all the numbers given, the greatest number should be the 1st number when arranging in descending order.
- Continue the same process for the rest of the given numbers.

**Example: **

Arrange the given numbers in the descending order 2564, 2478,3596

**Answer: **

Comparing the numbers it is clear that 3 > 2. So, the greatest number among these numbers is 3596.

The greatest number between 2564 and 2478 is 2564, as 5 > 4.

So, 3596 > 2564 > 2478

Hence, the descending order for the numbers will be 3596 ,2564, 2478.

**Formation of Greatest and Smallest Number from the Given
Digits**

- To form the greatest number, arrange the given digits from the highest to the lowest digit.
- To form the smallest number, arrange the given from the lowest to the highest digit.

**Example: **

Form the greatest digit from the given numbers 5, 7, 8.

**Answer: **

Form the given numbers 5, 7, 8

8 > 7 > 5

Hence, the greatest number is 875.

**Example: **

Form the smallest digit from the given numbers 5, 7, 8.

**Answer: **

Form the given numbers 5, 7, 8

5 < 7 < 8 .

Hence, the smallest number is 578.