Question

Write 0.135135.... in the form of p/q.

• A. 5/37
• B. 17/37
• C. 19/7
• D. 19/111

Answer 1

Answer:

A. 5/37

Let x = 0.135135.... ----(1) Multiply equation (1) by 1000, we have 1000x = 135.135.... ----(2) Subtract equation (1) from equation (2), we have 1000x - x = (135.135...) - (0.135135....) ⇒ 999x = 135 ⇒ x = 135/999 ⇒ x = 45/333 ⇒ x = 5/37