Question

Express a given rational number as a quotient of two integers: 0.1111111....

Answer 1

Any ideas?

Answer 2

@JeanneChristine Are you still there?

Answer 3

OpenStudy values the Learning process - not the ‘Give you an answer’ process
Don’t post only answers - guide the asker to a solution.

Answer 4

let a = 0.11111....
10a = 1.111111......
10a-a = 1
9a = 1
a=1/9

Answer 5

@rizwan_uet an elegant answer, but you should guide the asker to the answer instead of giving it to them.

Answer 6

I think technically speaking that if you have 0.1111 . . . (on and on) it's really 0.2

Answer 7

I think for the very reason that rizwan_uet solved the problem.

Answer 8

skullpatrol, yeah. When I was on here yesterday some kid was asking for the answer to a test question, while he was taking it. o.O

Answer 9

Peter14, I dunno about this particular question. I wouldn't have been able to be guided to the answer without seeing the answer that rizwan_uet gave.

Answer 10

suppose 2.02123123123................
we see that number 123 is repeated again and again.
Multiply R.H.S again and again by 10 till we get again123 .Here i do
Let x=2.02123123123....... ....(1)
10x=20.2123123123.......... .....(2)
100x=202.123123123....... .....(3)
1000x=2021.23123123...... .....(4)
10000x=20212.3123123...... .....(5)
100000x=202123.123123...... ....(6)
we see in (3) and (6) part after the decimal is same.
So subtract (3) from (6)
(100000-100)x=202123.123123......-202.123123...
99900x=201921
\[x=\frac{ 201921 }{99900 }\]