Question

How do you change $0.2$ into a fraction?

Answer 1

Hint:
Whenever they ask us to change a number from a decimal number to a fraction number, first think that decimal number out of $1$ . Usually in mathematics out of means division operation. Then multiply both the numerator and the denominator by $10$ and simplify the equation, you get the required answer.

Complete Step by Step Solution:
Whenever they ask us to change a number from a decimal number to a fraction number, first think that decimal number out of $1$ . Usually in mathematics out of means division operation.
Now, look at the given problem: they have asked us to change $0.2$ to fraction. As I said in the above, think of $0.2$ out of $1$ , which can be written as $\dfrac{{0.2}}{1}$.
In order to make the above form even simpler we can multiply both numerator and denominator by $10$. Which gives,
$\dfrac{{0.2}}{1} \times \dfrac{{10}}{{10}}$
We can multiply both numerator and denominator by $10$ only because $\dfrac{{10}}{{10}}$ gives $1$ .
On simplifying the above step we get
$ \Rightarrow \dfrac{{0.2}}{1} \times \dfrac{{10}}{{10}} = \dfrac{2}{{10}}$
The above equation can be simplified even more to arrive at the answer. That is both $2$ and $10$ are divisible by $2$ .
Therefore, $ \Rightarrow \dfrac{2}{{10}} = \dfrac{1}{5}$.

The fraction form of the decimal number $0.2$ is $\dfrac{1}{5}$.

Note:
The above problem can be solved in another way as well, that is when we have a decimal number, what the decimal number represents is each digit raised to a corresponding power of $10$ and if added together we get the required answer. The steps are shown as below:
$0.2 = 0 \times {10^0} + 2 \times {10^{ - 1}}$ Here, power is negative because it is after the decimal point. And this can be written as follows:
$ \Rightarrow 0.2 = 0 + 2 \times \dfrac{1}{{10}}$
$ \Rightarrow 0.2 = \dfrac{2}{{10}} = \dfrac{1}{5}$.