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10. interchange two digits of 54,687 to make it the:
a. smallest number. b. greatest number.

11. Think about the number of berths in the sleeper and AC coaches of a train. How many
berths will there be in 12 trains, each having 15 coaches?

ComPARiNg ANd oRdeRiNg NumbeRS

In order to compare two numbers, we adopt the following 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 64,36,680 and 6,56,485.
Solution. Place both the numbers in the TL L TTh Th H T O
place value chart.
6 4 3 6 6 8 0 7 digits
Thus, 64,36,680 > 6,56,485.
6 5 6 4 8 5 6 digits
Rule 2. Suppose we have to compare two
numbers with the same number of digits.

Step 1. First, compare the digits at the leftmost place in both the numbers.

Step 2. If they are the same, then compare the second digits from the left.

Step 3. If the second digits from the left are also the same, compare the third digits
from the left.

Step 4. Continue until you come across different digits in the corresponding places.
The number with the greater digit in that place is the greater of the two.

example 2. Which is greater: 5,27,691 or 9,54,639? L TTh Th H T O

Solution. 5,27,691 and 9,54,639 are 6-digit numbers. 5 2 7 6 9 1

We compare the leftmost digits of both numbers. 9 5 4 6 3 9

Since 5 < 9, 5,27,691 < 9,54,639.
example 3. Compare 87,94,365 and 87,89,973. different

Solution. Both numbers have 7 digits. So, first we compare
the leftmost digits of the two given numbers. TL L TTh Th H T O

The leftmost digits are the same. The second digits from 8 7 9 4 3 6 5
the left are also the same. 8 7 8 9 9 7 3
On comparing the third digits from the left, we find that

9 > 8. same different
So, 87,94,365 > 87,89,973.

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Large Numbers