Question

express 2.333....(irrational number) as a rational number​

Answer 1

Question:

Express 2.333....... as a rational number ( ie. in the form of p/q).

Answer:

7/3

Note:

• A rational number is a number in the form of p/q where p and q are any integer but q≠0 .

• There are two types of rational number:

1) Terminating rational number

2) Non-terminating but repeating OR

Non-terminating but recurring rational number

• Irrational number is a number which is Non-terminating and non-repeating .

Solution:

Let

x = 2.3333......... -------(1)

Now,

Multiplying both sides of eq-(1) by 10, we get;

10x = 23.3333....... ---------(2)

Now,

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

=> 10x - x = 23.333.... – 2.3333.......

=> 9x = 21

=> x = 21/9

=> x = 7/3

Hence,

The rational number form of the given decimal number (2.333.... ) is 7/3 .

Answer 2

Answer:

Suppose x = 2.333...(eq..1).

• Multiplying the both sides by 10 of (eq 1).

10x = 23.3333 ...( eq..2).

• Subtracting ( eq..1) by (eq...2).

= 10x - x = 23.333 ..- 2.3333 .

9x = 21.

x = 21 ÷ 9.

x = 7/3 .

Answer = 7/3 .