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EXAMPLE.1 Which is greater: 24576813 or 9897686? In 8-digit numbers, clearly 63890503 > 63872604 (9 T Th > 7 T Th).
SOLUTION: Here, we have to compare 24576813 and 9897686. In 7-digit numbers, clearly 5023145 > 4965328 (5 TL> 4 TL).
Clearly, 24576813 consists of 8 digits while 9897686 contains 7 digits. We know that a number
with more digits is greater. 24576813 > 9897686. The 6-digit number is 576943, which is clearly the smallest.

EXAMPLE.2 Which is greater: 96850374 or 96721895? 63890503 > 63872604 > 5023145 > 4965328 > 576943.
SOLUTION: Let us arrange the given numbers in a place-value chart, as shown below.
Hence, the given numbers in descending order are:
Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones 63890503, 63872604, 5023145.4965328, 576943.
ESTIMATION
9 6 8 5 0 3 7 4
Before estimation. we must know how to round off a number to the nearest ten. nearest hundred, nearest thou-
9 6 7 2 1 8 9 5 sand, etc. For the same, we need the rules given below:

Clearly, both the numbers have 8 digits. Rounding a Number to the Nearest Ten
Step 1: See the ones digit of the given number.
At the crores place both have the same digit, namely, 9. Step 2: If ones digit is less than 5, replace ones digit by 0, and keep the other digits as they are.
At the ten lakhs place both have the same digit, namely, 6. Step 3: If ones digit is 5 or more, increase tens digit by 1, and replace ones digit by 0.

But, at the lakhs place, the first number has 8 while the second has 7. Clearly, 8 > 7. Rounding a Number to the Nearest Hundred
96850374 > 96721895 Step 1: See the tens digit of the given number.
EXAMPLE 3. Arrange the following numbers in ascending order: Step 2: If tens digit is less than 5, replace each one of tens and ones digits by 0, and keep the other digits as
3763214,18340217,984671,3790423,18431056 they are.
SOLUTION: Let us arrange the given numbers in a place-value chart, as shown below. Step 3: If this digit is 5 or more, increase hundreds digit by 1 and replace each digit on its right by 0.

Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones Rounding a Number to the Nearest Thousand
Step 1: See the hundreds digit of the given number.
3 7 6 3 2 1 7 Step 2: If hundreds digit is less than 5, replace each one of hundreds, tens and ones digits by 0. and keep the
other digits as they are.
1 8 3 4 0 2 1 4 Step 3: If hundreds digit is 5 or more, increase thousands digit by 1 and replace each digit on its right by 0.We
9 8 4 6 7 1 may extend the ideas for larger numbers.

3 7 9 0 4 2 3
1 8 4 3 1 0 5 6 SOLVED EXAMPLES

Out of the given numbers one is a 6-digit number, two are 7-digit numbers and two are 8-digit numbers.
6-digit number is 984671. EXAMPLE 1: Round each of the following numbers to the nearest ten:
In 7-digit numbers we have 3763214 < 3790423. (a) 53 (b) 287 (c) 8364 (d) 2045
In 8-digit numbers we have 18340217 < 18431056.
Hence, the given numbers in ascending order are: SOLUTION: (a) In 53, the ones digit is 3 < 5.
984671 < 3763214 < 3790423 < 18340217 < 18431056. :. the required rounded number = 50.
(b) In 287, the ones digit is 7 > 5.
EXAMPLE 4. Arrange the following numbers in descending order: :. the required rounded number = 290.
63872604,4965328,63890503,5023145,576943 (c) In 8364, the ones digit is 4 < 5.
SOLUTION: Let us arrange the given numbers in a place-value chart. :. the required rounded number = 8360. (dl In 2045, the ones digit is 5 = 5.

Tens Crores Tens lakhs Ten Thousands Hundreds Tens Ones
Crores Lakhs Thousands EXAMPLE 2: Round each of the fallowing numbers to the nearest hundred:
6 3 8 7 2 6 0 4 (a) 648 (b) 2356 (c) 13768 (d) 1249

4 9 6 5 3 2 8
6 3 8 9 0 5 0 3 SOLUTION: (a) In 648, the tens digit is 4 < 5.

:. the required rounded number = 600.

5 0 2 3 1 4 5 (b) In 2356, the tens digit is 5 = 5.
5 7 6 9 4 3 :. the required rounded number = 2400.