Question

The decimal representation of the rational number is __________
1) Always terminating
2) Either terminating or repeating
3) Either terminating or non-repeating
4) Neither terminating nor repeating​

Answer 1

Answer:

2

Step-by-step explanation:

Decimal representation of rational numbers are either terminating for those fraction which has only multiples of 2 or 5 in denominator . i.e. they are of form

$\green{ \frac{x}{ {2}^{m} \times {5}^{n} } }$

Where m and n are integer . For example

$\frac{13}{50} = \frac{13}{ 2 \times {5}^{2} } = 0.26$

If denominator is not of this type then their decimal expansion is repeating for example

$\frac{22}{7} = 3. { \red{142857}142857....}$

The numbers whose decimal expansion is non repeating are called irrational . Here are few common examples of such numbers

$\pi = 3.142892653.... \\ e = 2.718281828.... \\ \sqrt{2} = 1.41421356237....$