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Express $0.1 7 ¯$ as a rational number and choose the option which represents the same.

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1691

845

1990

2290

answer is B.

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Detailed Solution

It is given the recurring decimal as

0.1 7 ¯

.
To express it in the form of

p q

, assume this number as, say x, and write in the expanded form as follows,

x = 0 ⋅ 177777.......

………... (i)
First, we shift 1 towards the left of the decimal, by multiplying each side of equation (i) by 10 as follows,

10 x = 1 ⋅ 77777.....

…………. (ii)
To shift the decimal point by one more place to the right multiply the equation (ii) by 10 on each side as follows,

100 x = 17 ⋅ 77777.....

…………(iii)
Now, subtract equation (ii) from (iii) and simplify as follows,

100 x − 10 x = 17.77777..... − 1.77777..... 90 x = 16 x = 1690 x = 845

From the above result, we can conclude that,

0.1 7 ¯ = 845

.
So, it is the required rational form.
Hence, the correct option is (2).

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