Answer

Verified

341.4k+ views

**Hint:**Fraction is 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,…

**Complete step by step solution:**

Take the given number: $0.312312....$

Let us suppose that

$x = 0.312\overline {312} $ ….. (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,

$1000x = 312.312\overline {312} $

The above equation can be re-written as –

$1000x = 312 + 0.312\overline {312} $

From equation (A), the above equation can be written as –

$1000x = 312 + x$

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 1000x - x = 312$

Simplify the above equation:

$ \Rightarrow 999x = 312$

Term multiplicative on one side, if moved to the opposite side then it goes to the denominator.

$ \Rightarrow x = \dfrac{{312}}{{999}}$

Find the factors of the above term

$ \Rightarrow x = \dfrac{{104 \times 3}}{{333 \times 3}}$

Common multiple from the numerator and the denominator cancel each other.

$ \Rightarrow x = \dfrac{{104}}{{333}}$

**This is the required solution.**

**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. Equations should be converted in the form of equivalent. To convert decimal into fraction, place the decimal number over its place value. For example, for $0.6$ the six is in the tenths place so that we place $6$ over $10$ to create the equivalent fraction i.e. $\dfrac{6}{{10}}$

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

What happens when entropy reaches maximum class 11 chemistry JEE_Main

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Distinguish between the reserved forests and protected class 10 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give simple chemical tests to distinguish between the class 12 chemistry CBSE

Difference Between Plant Cell and Animal Cell

Which of the following books is not written by Harshavardhana class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

In which states of India are mango showers common What class 9 social science CBSE

What Made Mr Keesing Allow Anne to Talk in Class class 10 english CBSE