Question

answer plzjsfsmshsbs if s GB h​

Answer 1

Answer:

0.333... = 1/3

Note:

• Rational number : The number which can be written in the form of p/q where p and q are integers but q ≠ 0 is called rational number.

• Rational number is characterized as :

1) Terminating

2) Non-terminating but repeating

( or Non-terminating but recurring )

• Every terminating decimal and Non-terminating but repeating decimals can be written in the form of p/q .

Solution:

Let us suppose,

x = 0.333... ---------(1)

Multiplying both sides of eq-(1) with 10 ,

We get ;

=> 10•x = 10•(0.333...)

=> 10x = 3.333... --------(2)

Now,

Subtracting eq-(1) from eq-(2) , we get ;

=> 10x - x = 3.333... – 0.333...

=> 9x = 3

=> x = 3/9

=> x = 1/3

=> 0.333... = 1/3 { since , x = 0.333... }

Hence,

0.333... = 1/3 , which is in the form of p/q , when p = 1 and q = 3 . ( Clearly , p and q are integers and q ≠ 0 )