Question

0.001 bar is equal to
(a) 1/1000.
(b) 1/999.
(c) 1/990.
(d) 1/99.

{ALIGARH MUSLIM UNIVERSITY +2 ENTRANCE TEST 2008-09}

Answer 1

HELLO DEAR,

LET X= 0.001

bar=0.001001001......
and ,
1000x = 1.001001.....

subtracted x from 1000x

1000x = 1.001001.....
— X = 0.001001001....


999X= 1.000000.......

X = 1/999
I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Hi there!
To convert recurring or repeating decimals into some rational fraction we will assume that recurring number as x and then will try to find which digits r repeating.Will shift those digits to left hand side of our first equation. Then will substract the 2 equations formed and then make subject as x to obtain your answer.
Let
x=0.001 bar=0.001001001...(it will continuously go on till infinity)

1000x =1.001001001.............(same for his too)( did you observe 001 is repeating so to move it LHS we multiply 1000)
substract ing above 2 equation

subtract x from 1000x
and

substract 1.001001001...-0.001001001..

so  999x = 1.000000000
X=b options