Teachers
Eligibility Test  Paper 2
Class – VI Mathematics
NUMBER SYSTEM
Comparison
of Numbers
Comparing numbers with unequal number of digits:
1.
When we compare two numbers 16090 and 100616, we have already learnt that the number
with more digits is greater.
Hence, 1,00,616 (6 digit number) > 16,090 (5 digit
number).
2.
Suppose we are given more than two numbers say 1468, 5, 201, 69 and 70000.
Then among these, we can immediately
say that the number 70000 is the greatest and 5 is the least, based on the
number of digits.
E.g.:
1.
Write the numbers in the ascending order: 688, 9, 23005, 50, and 7500.
Answer:
9,50,688,7500,23005.
2.
Find the least and the greatest among the numbers: 478, 98, 6348, 3, 6007,
50935.
Answer: Least number 3
Greatest number  50935
Comparing numbers with equal number of digits
Compare the given
numbers 2180 and 2158
2=2 
1=1 
8>5

Hence,2180 > 2158.
Example:
Compare 59283746
and 59283748 using place value chart.
Solution:
Step 1: Number
of digits in the two given numbers are equal.
Step
2: Compare the place values using the place value chart.
Place Value 
C 
T L 
L 
T Th 
Th 
H 
T 
O 
First Number 
5 
9 
2 
8 
3 
7 
4 
6 
Second Number 
5 
9 
2 
8 
3 
7 
4 
8 
Compare the
digits of the two numbers from the highest place value as noted below.
5 = 5, 9 = 9, 2
= 2, 8 = 8, 3 = 3, 7 = 7, 4 = 4, 6 < 8
Here only the
digits in the ones place are not equal and 6 < 8.
Hence,59283746
< 59283748.
DO YOU KNOW? The number 10100
is
called googol (this is, 10 multiplied 100 times) The
number 10googol = 10(10^{100})
is
called googolplex. 
Arranging
the numbers in ascending and descending order:
Example:
Arrange the
following numbers in the descending order:
128435,
10835, 21354, 6348, 25840
Answer:
128435 > 25840 > 21354 > 10835 > 6348
Creating
New Numbers:
Using the four digits 9, 4, 8 and 5 we need
to make different 4digit numbers in such a way that the digits are not
repeated. We get the following arrangement of different 4digit numbers.
Th 
H 
T 
O 
9 
4 
8 
5 
9 
4 
5 
8 
9 
8 
4 
5 
9 
8 
5 
4 
9 
5 
4 
8 
9 
5 
8 
4 
Example:
Raja
writes a 3digit number, using the digits 4, 7 and 9. What are the possible
numbers he can write?
Answer:
4 
7 
9 
4 
9 
7 
7 
4 
9 
7 
9 
4 
9 
4 
7 
9 
7 
4 
Hence
the numbers are 479,497,749,794,947,974.
Impact
of Place Value
Consider
the 4digit number 3795. When we exchange the digits of two places, the number
either becomes larger or smaller. For example, the given number is 3795. If the
digits 9 and 5 are exchanged, then the number is 3759. This number is less than
the given number. It makes a great impact in the situations like handling
currencies.
Example:
Postal
Index Number consists of six digits. The first three digits are 6, 3, and 1.
Make the largest and the smallest Postal Index Number by using the digits 0,3
and 6, each only once.
Answer:
The smallest
Postal Index Number is 631036.
The largest Postal Index Number is 631603.
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