Question

Convert the fraction $\dfrac{1}{6}$ into simple decimal recurring form.
(a) $0.1\bar 9$
(b) $0.1\bar 6$
(c) $0.1\bar 4$
(d) $0.1\bar 3$

Answer 1

Hint: As we know that the given question is in fraction and we have to convert it in simple decimal recurring form. We know that a repeating decimal or recurring decimal is a decimal representation of a number whose digits whose digits are repeated continuously. A decimal fraction in which all the numbers after the decimal point are repeated is called a pure recurring decimal.

Complete step by step solution:
AS per the given question we have fraction i.e. $\dfrac{1}{6}$. At first we will convert the fraction into decimal and then analyse the number. And we know that a pure recurring decimal is a decimal fraction in which all the figures after the decimal point are repeated.
We can write the fraction in decimal form: $\dfrac{1}{6} = 0.166666666...$
AS we can see that the number $6$ after the decimal is repeating continuously, so we can say it as pure recurring decimal. We can write it as $0.1\bar 6$.
Hence the correct option is (b), $0.1\bar 6$.

Note: We should note that in a recurring decimal, if a single number is repeated, then it is expressed by putting a dot on it. And if a set of numbers are repeated as in the above solution of the question, then it can be expressed by putting a bar on the set, as we did in the above number. We should always try to convert the fraction in the simplest form as it is easy to give the result.