Question

How does 0.2 convert to $\dfrac{1}{5}$?

Answer 1

Hint: According to the question, to convert the decimal number into the fraction, firstly we have to count the number of digits after the decimal point. And, then proceed to remove the decimal into fraction.

Complete step by step answer:
First we will write the steps to convert a decimal to a fraction:
Step 1: Write down the decimal as a fraction of one;
Step 2: If the decimal is not a whole number, multiply both top and bottom by 10 until we get an integer at the numerator.
Step 3: Simplify(or reduce) the fraction if it is not in the simplest form.
Now,
The given decimal number is $0.2$.

To convert the decimal $0.2$ to a fraction, we will go through the steps as follows:-
Step-1: Write down the given decimal number as a fraction of one:
$0.2 = \dfrac{{0.2}}{1}$
Step-2: Multiply both numerator and denominator of the above fraction by 10 for every number after the decimal point. And, we have two digits after the decimal points, so we multiply both numerator and denominator by 10.
So,
$\dfrac{{0.2}}{1} = \dfrac{{0.2 \times 10}}{{1 \times 10}} = \dfrac{2}{{10}} = \dfrac{1}{5}$
This fraction is already in proper form, so we cannot reduce it any further.

Hence, the fraction of $0.2$ is $\dfrac{1}{5}$. That’s how, we can convert 0.2 into $\dfrac{1}{5}$.

Note: In fraction numbers, when the numerator is greater than the denominator then the fraction is called Improper Fraction and we can convert it into mixed fraction by dividing the numerator from denominator.