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Express $3. 1 ¯ 4 ¯$ as a rational number and choose the option which represents the same.

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31199

31299

313999

315999

answer is A.

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Detailed Solution

It is given the recurring decimal as

3. 14 ¯

.
To express it in the form of

p q

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

x = 3 ⋅ 141414.......

………... (i)
To shift the decimal point by two places to the right, multiply the equation (i) by 100 on each side as follows,

100 x = 314.141414.....

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

100 x − x = 314.141414..... − 3.141414..... 99 x = 311 x = 31199

From the above result, we can conclude that,

3. 14 ¯ = 31199

.
So,

31199

is the required fraction for

3. 14 ¯

.
Hence, the correct option is (1).

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