TET Syllabus - Mathematics Study Materials in Number System (Part II)

 

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(10100) 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 4-digit numbers in such a way that the digits are not repeated. We get the following arrangement of different 4-digit 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 3-digit 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 4-digit 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.