1st Class Mathematics Comparison of Numbers Introduction

Introduction

Category : 1st Class

* Introduction 

 

Comparison enables us to identity what is greater or smaller between two objects and what is greatest and smallest among more than two objects.

For example, if we compare&, it is clear thatis bigger number but if we compare

& then

is the smallest andis the biggest number.

Whilecomes between&therefore, it is greater or bigger than but smaller or less than.  

 

 

*  Comparison of Numbers

Let us see the given below examples:  

 

 

 

It means thatis greater thanand '>'is the sign of 'greater than' or bigger than 'or more than' 

is read as:

(a) is greater than

(b) is bigger than

(c) is more than

is also written asand read asis less than

Therefore, it is clear that the mouth of the sign '>' is open to the side of the greater or bigger number.  

 

 

Howis a greater number betweenand 3?

For that we apply vertical line trick:  

 

When countedis more than

Hence Take another example:  

 

 

Which one is bigger betweenand?

Clearlyis more than

or  

 

 

 

and or

It means the numberhas two digits and the numberhasdigit. Therefore,is greater than Take another example:  

 

 

If we compareand Then:

or

has three digits andhas two digits. Therefore,is greater than.

If the two numbers have equal number of digits then the digits at extreme left are compared and the number with greater digit is greater.  

 

 

If we compareandthen:

or

To find this result we compare the two numbers.

While comparing two digit numbers, if extreme left digits are equal or same then we compare the next digits to the right and so on. In this case also the number with greater digit is greater.  

 

 

When we compare and or  

Therefore,  

 

 

  

 

  1.  Which one of the given below options is false?

(a)1 > 9

(b) 4 > 3                                               

(c) 5 > 3

(d) 9 > 8

 

Answer: (a)

Explanation

Option (a) is correct because:

 

Hence,

Option (b) is incorrect as it is true. Let's check:

Hence,

Option (c) is incorrect as it is true. Let's check:

Hence,

Option (d) is incorrect as it is true. let us check:

Hence,  

 

 

 14 > 10 will be read as____.

(a) 10 is greater than 14                

(b) 14 is less than 10

(c) 10 is bigger than 14                  

(d) 14 is greater than 10  

 

Answer: (d)

Expiation

is read as "14 is greater than 10"

 

*  Smaller Numbers

See the following examples:  

 

 

It meansis less than 3 and '<' is the sign of 'less than' or 'smaller than'.

Hence,is read as:

(a) is smaller than

(b) is less than

is also written as. So it is clear that the mouth of the sign '<' is closed to the side of the smaller number. Howis smaller in?

For this, Let's see the vertical line trick:

When countedis less than

Hence,

Take another example:  

 

 

Which one is smaller when andare compared?

Here we have

Clearlyis less than

Hence, or  

 

 

* Other Rules  

Rule 1: If a number has less digits than another, it is smaller of the two. If we haveand Then or

Let us take another example:

If we compareand

Then or  

Rule2: If the two numbers have equal number of digits then the digits on extreme left are compared and the number with smaller digit is smaller. Whenandare compared thenis true.

To know how is it possible just see the trick given below:

Thus And hence,  

 

Rule3: While comparing two digit numbers, if extreme left digits are same then we compare the second digit from left. In this case also, the number with smaller digit is smaller.

When we compareand

Then

or

Trick:

Here

Hence,  

 

 

  

 

 Just see the numbers inside the egg given below and find out which one is the smallest?

(a) 15                                                    

(b) 16

(c) 10                                                    

(d) 9  

 

Answer: (d)

Explanation

The only single digit number given. Rest of the options is incorrect because they are double digit numbers and therefore, bigger than  

 

 

  Which one is wrong?

(a)                              

(b)

(c)                               

(d)  

 

Answer: (d)

Explanation

Option (d) is correct because it is wrong.

Let's check

Hence,or

Option (a) is incorrect because it is true.

Let's check:

Hence, Option (b) is incorrect because it is true. In fact 2 digits number 10 is greater than 5.

Option (c) is incorrect because it is true Let's check:

 

 

Hence, or  

 

 

*  Equal Numbers  

Equal means neither greater nor less than.

Let's consider

and  

These numbers are equal because if one or more zeroes is put before any number, the number remains unchanged. Thusandcan be written as:

or  

Where '=' is the sign of equal

And  is read as,

is equal to  

Similarly take another example:

andis equal and they can be written as

or  

 

 

 

 

 

  Which one of the following pair of numbers is not equal?

(a) 2 and 02                                        

(b) 02 and 2

(c) 002 and 2                                      

(d) 20 and 2

 

Answer: (d)

Explanation

is a double digit number andis a single digit number. So.  

 

 

 Choose the incorrect statement.

(a) 05 and 5 are equal                    

(b) 60 and 06 are equal

(c) 07 and 007 are equal               

(d) 08 and 8 are equal

 

Answer: (b)

Explanation

is equal toandor  

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