Answer to Question #12761 in Algebra for rangan

Question

.99999999999999=1 is true or not.............

Answer 1

0.99999999999999 ≠ 1 cause 1 - 0.99999999999999 = 0.00000000000001 ≠ 0.

But 0.99999999999999..... = 0.(9) = 1. Here is the proof.

Let
x = 0.99999999999999...
So
10x = 9.9999999999999999...

Subtract the first equation from that last one:

9x = 9.0000000000000000000...

At last,

9x = 9 ==> x = 1.