Answer

Verified

389.7k+ 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

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE