Question

The value of $ 0.\overline {35} $ is equal to
A. $ \dfrac{{35}}{{66}} $
B. $ \dfrac{{35}}{{77}} $
C. $ \dfrac{{35}}{{99}} $
D.None of these

Answer 1

Hint: Fraction can be defined as the number when represented in the form of the numerator upon the denominator. Here we will take the given number and will suppose using some variable. Variables are terms expressed using the small alphabets such as x, y, z,…here bar on the number represents the recurring terms

Complete step-by-step answer:
Take the given number: $ 0.\overline {35} = 0.353535 $
Let us suppose that
 $ x = 0.3535\overline {35} $ ….. (A)
 (it is given that it is repeating)
Repeating means the number repeated again and again. It is also known as recurring numbers.
Take the equation (A) and multiply both the sides of the equation with the number
Then,
 $ 100x = 100 \times 0.3535\overline {35} $
 $ 100x = 35.35\overline {35} $
The above equation can be re-written as –
 $ 100x = 35 + 0.35\overline {35} $
From equation (A), the above equation can be written as –
 $ 100x = 35 + x $
Take a variable on the left hand side of the equation. When you move any term from one side to another then the sign of the term also changes. Positive term changes to the negative term and vice-versa.
 $ \Rightarrow 100x - x = 35 $
Simplify the above equation:
 $ \Rightarrow 99x = 35 $
Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow x = \dfrac{{35}}{{99}} $
Hence, from the given multiple choices option C is the correct answer.
So, the correct answer is “Option C”.

Note: Always remember that when you multiply any term on one side of the equation, it should be multiplied on both the sides of the equation only. Equations should be converted in the form of its equivalent expression. To convert decimal into fraction, place the decimal number upon its place value. For example, for $ 0.6 $ the six is in the tenths place so that we place $ 6 $ upon $ 10 $ to create the equivalent fraction i.e. $ \dfrac{6}{{10}} $