Question

8. Express the . 233333…. in the form of where p and q are integers and q≠0 .

Answer 1

I am just doing this for points sorry

Answer 2

To Express :

• Express the . 233333…. in the form of where p and q are integers and q≠0 .

Solution :

Let x = 0.2333... since one digit is repeating, we multiply x by 10 to get :

• 10x = 2.3...
• 10x = 2.1 + 0.23 = 2.1 + x
• 10x = 2.1 + x
• 10x - x = 2.1
• 9x = 2.1
• x = 2.1/9
• x = 21/9 × 10
• x = 21/90

Therefore :

• So p/q form of 0.2333.. is 21/90

Summary :

• Every number with non terminating recurring decimal expansion can be expressed in the p/q form where (q ≠ 0) and p and q are integers.
• The decimal expansion of rational number is either terminating or non terminating recurring. Moreover, a number whose decimal expansion is terminating or non terminating recurring is rational.

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