18
Dec
09

Solutions to WU’s puzzles and riddles : .999 … (medium)


0.999 = 1

I am trying to find all the solutions and put them together at a single place, So feel free to add comments and if you have a solution please do post. Cheers …🙂

Here is the puzzles link : http://www.wuriddles.com/

Question :

Compare the numbers 0.99999… (infinitely many 9s) and 1. Which of the following statements is true? Why?

* 0.99999 … < 1

* 0.99999 … = 1

* 0.99999 … > 1

My Solution : There are different approaches to this problem. And the answer is 0.999 = 1

First Approach:

3/3 = 1                         =>                3 X (1/3) = 1

3 X (0.33333) = 1                 =>                     0.999999 =1

Second Approach :

0.9999999999  =  9 X (0.111111111)

But 0.11111111 = 1/9

There fore 9 X (0.111111111) = 9 X 1/9 = 1

Third Approach:

Lets say x = 0.9999999999999   —————– > (1)

then 10x = 9.999999999999    —————– > (2)

Now subtract (1) from (2)

Then we get 10x – x = 9

=> 9x = 9

=> x = 1 ……😀


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