Question

Convert $0.2$ into fraction.

Answer 1

Hint: In this question we have to convert a given number into a fraction. The given number is in the form of a decimal number which is a number which consists of two parts, an integer part and a fractional part. The number before the decimal has an integer number and the numbers after the decimal numbers represent values smaller than one. We will convert it into a fraction by multiplying and dividing the number by $10$ to remove the decimal point and simplify it to get the required solution.

Complete step by step answer:
We have the number given to us as:
$\Rightarrow 0.2$
Now in our decimal number there are two places after the decimal and one integer value before the decimal. Since there are two decimal places, we will multiply the number by ${{10}^{1}}$ which is $10$, to remove the decimal and get the entire number in integer form. Now since we are multiplying the number by $10$, we will also divide the number by $10$ so that its value does not get changed.
On multiplying and dividing by $10$, we get:
$\Rightarrow 0.2\times \dfrac{10}{10}$
On multiplying the terms, we get:
$\Rightarrow \dfrac{2}{10}$
Now the above fraction can be written as:
$\Rightarrow \dfrac{2\times 1}{2\times 5}$
On cancelling the common term $2$, we get:
$\Rightarrow \dfrac{1}{5}$, which is the required solution.

Note: In this question we have the fraction in the form of a proper fraction. A proper fraction is a fraction in which the numerator is smaller than the denominator. There also exists improper fraction which has its numerator greater than the denominator and mixed fraction which consists of two parts which are a whole number and a fraction part.