Question

The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form `p/q`, what can you say about the prime factors of q? (i)`43. 123456789` (ii) `0.120120012000120000` (iii) `43.overline(123456789)`

Answer 1

(i) Rational
only if denominator = `2^a5^b ; (a,b in N)`
`2 and 5 ` only
(ii) irrational
(iii) rational
`q = 2^2*5^b..... ; 43+ 12345678/999999999 `
answer