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COMPARING AND ORDERING NUMBERS

In order to compare two numbers, we follow the following rules:

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

Solution: Place both the numbers in place value chart.
Clearly, the given numbers are of 8- and C TL L TTh Th H T O
7-digit numbers, respectively. 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. Then, we follow the following
steps to compare the numbers.

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

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

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

So, we compare the left-most digits of both 5 5 2 7 6 9 2
numbers. Since, 5 > 3 3 9 5 4 6 3 5
Hence, 5527692 > 3954635.

Example 3: Compare 9794362 and 9789974. Different
Solution: Both numbers are of 7 digits. TL L TTh Th H T O
So, first, we compare the left-most digits of
the two given numbers. 9 7 9 4 3 6 2

First left-most digits are same, i.e., 9. Now, 9 7 8 9 9 7 4
compare second left-most digits.
Second left-most digits are also same, i.e., 7. Same Different (9 > 8)

Now, comparing third left-most digits, here 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 number among the given numbers.

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