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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

comParing anD orDering numbers

In order to compare two numbers, we follow these rules:

Rule 1: If two numbers have a different number of digits, the number with fewer digits is
smaller than the number with more digits.
Example 1: Compare 46436680 and 8656484.

Solution: Place both the numbers in the place value chart.
Clearly one number has 8 digits and the C tL L TTh Th H t O
other number has 7 digits. 4 6 4 3 6 6 8 0 8 digits

Thus, 46436680 > 8656484. 8 6 5 6 4 8 4 7 digits
Rule 2: If two numbers have the same number of digits, follow these steps to compare the
numbers:

Step 1: First, compare the digits at the leftmost place in both numbers.
Step 2: If they are the same, then compare the digits at the second place from the left.

Step 3: If the second digits from the left are also the same, compare the digits at
the third place from the left.
Step 4: Continue until you come across different digits at the corresponding places.
Now, the number with the greater digit at this place will be the greater number.

Example 2: Which is greater: 5527692 or 3954635?
Solution: Here, both numbers have 7 digits. tL L TTh Th H t O

So, comparing the leftmost digits of both 5 5 2 7 6 9 2
numbers, we get 5 > 3. 3 9 5 4 6 3 5
Hence, 5527692 > 3954635.

Example 3: Compare 9794362 and 9789974. Different
Solution: Both numbers have 7 digits. tL L TTh Th H t O
So, first, we compare the leftmost digits of
the two given numbers. 9 7 9 4 3 6 2

The leftmost digits are the same, i.e., 9. Now, 9 7 8 9 9 7 4
compare the second digits from the left.
These digits are also the same, i.e., 7. Same Different (9 > 8)

Now, comparing the third digits from the left, we get 9 > 8.
So, 9794362 > 9789974.

Example 4: Arrange the following numbers in ascending order:
53072249, 51889620, 86121450, 27504545, 983250

Solution: Let us arrange the given numbers in the place value chart.
Here, we can see that there are four 8-digit numbers and one 6-digit number.

Clearly, the 6-digit number is the smallest.

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