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Q.

The simplest form of 1. 6 ¯   is


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a

833 500  

b

8 5  

c

5 3  

d

None of these 

answer is C.

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Detailed Solution

Given is a recuring decimal, 1. 6 ¯  .
To express it in the form of p q  , assume this number as, say x, and write in the expanded form as follows,
x=1⋅66666.......                           ……….. (i)
We shift the decimal by 1 place towards the right by multiplying each side of equation (1) by 10 as follows,
10x=16⋅66666.....                   …………. (ii)
Now, subtract equation (i) from (ii) and simplify as follows,
10x−x=16.66666.....−1.66666..... 9x=15 x= 15 9 x= 5 3  
From the above result, we can conclude that,
1. 6 ¯ = 5 3  .
Hence, the correct option is (3).
 
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The simplest form of 1. 6 ¯   is