Comparing Numbers

"Imagine you're comparing your test scores with your friends: 89, 92, 76, 89. Which score is the highest? Which is the lowest? Learning to compare numbers helps us understand which quantities are bigger or smaller - whether it's money, distances, or even temperatures!"

Rule 1: Comparing by Number of Digits

• The one with more digits is greater.

Examples:

• 62,000 and 5,293 → 62,000 has more digits → 62,000 is greater.
• 24,522 and 8,899 → 24,522 has more digits → 24,522 is greater.
• 34,687,300 and 2,392,460 → 34,687,300 has more digits → it's greater.

Rule 2: If the numbers have the same number of digits
Step 1: Compare the first digit.

• Greater first digit → Greater number

Examples:

• 87 and 69 → 8 > 6 → 87 is greater.
• 3297 and 2988 → 3 > 2 → 3297 is greater.
• 8,20,797 and 6,90,824 → 8 > 6 → 8,20,797 is greater.

Step 2: If the first digits are the same, compare the second digit.

• Greater second digit → Greater number.

Examples:

• 4537 and 4289 → first digits 4 = 4; compare second: 5 > 2 → 4537 is greater.
• 5,62,789 and 5,32,999 → first 5 = 5, second 6 > 3 → 5,62,789 is greater.

Step 3: If the first and second digits are the same, compare the third digit.

• Greater third digit → Greater number.

Examples:

• 9832 and 9823 → 9 = 9, 8 = 8, 3 > 2 → 9832 is greater.
• 536250 and 534798 → 5 = 5, 3 = 3, 6 > 4 → 536250 is greater.
• 8224327 and 8254327 → 8 = 8, 2 = 2, 2 < 5 → 8254327 is greater.

Example 1:
Use table form to compare the numbers 6,45,824, 23,78,926, 3,28,792 and 6,54,284 and write the given numbers in descending order.
Solution:
The required table is as given below:

Clearly, given numbers in descending order are as follows:
23,78,926 > 6,54,284 > 6,45,824 > 3,28,792. 

Example 2:
Find the greatest and smallest in each group:
(i) 573, 8294, 37, 54908, 1036

• 54908 = most digits → greatest
• 37 = least digits → smallest

 Answer: 54908 is the greatest, and 37 is the smallest.

ii) 2483, 79312, 103, 4078, 573

• 79312 = most digits → greatest
• 103 and 573 = both 3 digits → compare → 103 < 573

 Answer: 79312 is the greatest, and 103 is the smallest.

Out of any two numbers marked on a number line, the number which is

1. to the right is greater
2.  to the left is smaller. 

Considering the number line drawn above:

1. 3 > 1 (3 is to the right of 1)
2. -2 > -5 (-2 is to the right of -5)
3. 0 > -3 (0 is to the right of -3)

Thus, each number on a number line is always greater than each and every number to its left. Similarly, each number on a number line is always smaller than each and every number to its right. 

1. Two schools collected money for charity: School A collected ₹45,678 and School B collected ₹45,734. Which school collected more?

• Both have five digits.
• Compare: 45,678 vs 45,734
• First three digits are the same: 4 = 4, 5 = 5
• Fourth digit: 6 < 7 → School B collected more money!

2. Scenario: Your class is organising a book collection drive. Three sections of collected books:

• Section A: 1,245 books
• Section B: 1,254 books
• Section C: 1,204 books

Question: Which section collected the most books? Arrange in descending order.
Solution:
All have four digits, so compare using place value:

• Compare 1,245 and 1,254: 1,254 > 1,245 (5 > 4 in tens place)
• Compare 1,254 and 1,204: 1,254 > 1,204 (5 > 0 in tens place)
• Compare 1,245 and 1,204: 1,245 > 1,204 (4 > 0 in tens place)

Answer: Section B collected the most. Order: 1,254 > 1,245 > 1,204

• More digits = Greater number
• Number line: Right = Greater, Left = Smaller
• Symbols: > (greater than), < (less than), = (equal to)
• For negative numbers:-2 > -5 (closer to zero is greater)