Math, asked by TbiaSupreme, 1 year ago

0.090909...=0.09,Given real number is expressed in decimal form. Find whether they are rational or not. If rational, express them in the form p/q. Comment on factors of q.

Answers

Answered by nikitasingh79
28

REAL NUMBERS :

a number which is either rational or irrational is called a real number.

RATIONAL NUMBERS :

A number that can be expressed as p/q , where p,q are Integers and q≠0 is called a rational number.

IRRATIONAL NUMBERS :

A number that cannot be expressed as p/q , where p,q are Integers and q≠0 is called a irrational number.

NON TERMINATING REPEATING DECIMAL EXPANSION :

The number which does not terminate but repeat the particular number again and again in the process of division , is said to be a non terminating repeating decimal expansion.

SOLUTION :

Given : 0.090909...=0.09

0.09 non terminating recurring ,so it is a rational number.

Let x = 0.090909……(1)

Multiply equation 1 by 100

100 × x = 100 × 0.090909…

100x = 9.0909….. … (2)

Subtract equation 1 from 2

99 x = 9

x = 9/99

x =1/11

Hence, 0. 090909...=0.09 is a rational number.

HOPE THIS ANSWER WILL HELP YOU...

Answered by mysticd
7
Hi ,

0.090909.... = 0.09 bar ( bar on 09 )

Period = 09

periodicity = 2

0.909090... is a retional number.

Since , it is a non terminating

repeating decimal .

ii ) Let x = 0.090909.... ---( 1 )

multiply equation ( 1 ) with 100 , we get

100x = 9.090909..... ( 2 )

Subtract equation ( 1 ) from ( 2 ) ,

we get

99x = 9

x = 9/99

x = 1/11 [ p/q form ]

Therefore ,


x = 0.0909.... = 1/11

I hope this helps you.

: )


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