Tag: real number

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.
Here, $5$ divided by $8$ gives $0.625$.

$\displaystyle \frac { 2 }{ 7 }  = 0.285714285.. = 0.\overset { \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _ \ _  }{ 285714 } $

The value of $\displaystyle \frac { 3 }{ 11 }$ is $ 0.272727272727.. 0.\overset { \ _ \ _ \ _ \ _  }{ 27 } $

While expressing a fraction in the decimal form, when we perform division we get some remainder. 

A terminating decimal is a decimal that ends. It's a decimal with a finite number of digits.

$2\displaystyle \frac { 1 }{ 6 }  = \frac { 13 }{ 6 }  = 2.166666666.. = 2.1\overset { \ _ \ _  }{ 6 } $

$\frac {65}{455}=0.\overline { 142857 } $
Therefore, the decimal representation will be non-terminating repeating.

$\displaystyle \frac { 5 }{ 6 }= 0.83333333..= 0.8\overset { \ _ \ _  }{ 3 } $ 
This is a pure recurring decimal as $3$ is repeated continuously.

Write the decimal number as a fraction $0.2020020002...... $
It is Non- terminating decimal and cannot be represented as a quotient of two integers.
Therefore, B is the correct answer.

We know $\dfrac{7}{4}=1.75$