Representing a strange number as a fraction

Question

Can this decimal with special patterns be expressed as a fraction? Is it a rational number?

$$0.101001000100001000001...$$

Where the number of zeros after every 1 is increased by 1.

Ty.

score 3 · Accepted Answer · answered Sep 26 '13 at 07:17

3

It is an irrational number, since it does not have a periodic decimal expansion. Hence it cannot be expressed as a fraction of two integers.

answered Sep 26 '13 at 07:17

Thanks man for the clarification! – Commander Shepard Sep 26 '13 at 07:20
1

are you really a Ph.D student at the age of 20? Just wondering – Commander Shepard Sep 26 '13 at 07:23

1 Answers1