Question

Express 1.8181… in the form p/q where p and q are integers and q ≠ 0.

Answer 1

Explanation:

Let x=1.8181...-----(1)

Here periodicity is 2

So,we should multiply x with 100

⇒100×x=100×1.8181....

⇒100x=181.8181...------(2)

(2)-(1),

⇒100x=181.8181...

(-) x=001.8181...

⇒99x=180.0000

⇒x=180/99

∴The p/q form of 1.8181... is 180/99.