Question

write the rational number 2 /11 in decimal form identify the rational number is recurring decimal form or terminating decimal form​

Answer 1

Step-by-step explanation:

Without actual division one can check a given rational number is terminating decimal expansion if its denominator can be written in form of 2^n5^m2

n

5

m

Here, given rational number is \frac{2}{11}

11

2

.

Denominator is 11 so, it cannot be written in form 2^n5^m2

n

5

m

.

Thus, \frac{2}{11}

11

2

has a non-terminating repeating decimal expansion.

Also , below attachment justifies this,

\frac{2}{11}=0.18181818..

11

2

=0.18181818..

Answer 2

Given:

$\frac{2}{11}$

For convert it into decimal form divide 11 by 2

     0. 8 1  8 1        

11 ) 20

   - 11

      90

     - 88

        20

       - 11  

         90

       - 88

          20

         - 11  

           9

Here, 0.18   is block of digits that repeats.

∴ This is non-terminating

Because of repeating term 0.1818 it is repeating decimal form

Hence it is recurring decimal form