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CBSE Class 7 Answered

Dear Sir -  How can we convert non terminating decimal number 0.99999.... into a fraction? I used long method but get 9/9 which is not correct..
Asked by Aashish | 13 Apr, 2016, 10:12: PM
answered-by-expert Expert Answer
We know that 0.99999.... is approximately equal to 1.
 
So, 9/9 you got using long division method is correct. As 9/9 = 1
 
Another method of solving the same is :
 
Let 0.99999...... = x
Then 10x = 9.99999.....
Subtracting x from 10x we get, 
 
10 x space equals space 9.99999.....
bottom enclose negative x equals space space 0.99999.... end enclose
9 x space equals space 9
x space equals space 9 over 9 equals space 1
 
Hence, 0.99999...... = 1
 
 
Answered by Keravi Thanani | 15 Apr, 2016, 11:19: AM
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