State true or false: The rational form of $0 . \underset{̲}{3}$ is $13$ .

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True

False

answer is A.

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Detailed Solution

Given is the recurring decimal,

0 . \underset{̲}{3}

.
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 ⋅ 33333.......

……….. (i)
We shift the decimal by 1 place towards the right by multiplying each side of equation (1) by 10 as follows,

10 x = 3 ⋅ 33333.....

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

10 x − x = 3.33333..... − 0.33333..... 9 x = 3 x = 39 x = 13

From the above result, we can conclude that,

0. 3 ¯ = 13

.
Hence, the given statement is true.
So, the correct option is 1.

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