Question

How do you convert $0.204$ into a percent and fraction?

Answer 1

Hint: In this question we have been given a number which is in the decimal form which we have to convert into a percentage and a fraction. We know that the percentage of a number represents the number in terms of a fraction which is divided by $100$. Therefore, we will use cross multiplication to get the number in the percentage form. To get the number as a fraction we will use the decimal number and remove the decimals by multiplying and dividing the number by $1000$ and simplify it to get the required solution.

Complete step by step solution:
We have the number given to us as:
$\Rightarrow 0.204$
We can see that the number is in the decimal form. Now to convert it into a percentage we have to find a number $\dfrac{x}{100}$ such that it is equal to the value $0.204$.
On equating, we get:
$\dfrac{x}{100}=0.204$
On transferring $100$ from the left-hand side to the right-hand side, we get:
$x=0.204\times 100$
On simplifying, we get:
$x=20.4\%$, which is the required number in percentage form.
Now to get the fraction form of the number, consider the given number:
$\Rightarrow 0.204$
Now since there are $3$ decimal places, we will multiply and divide the term with $1000$.
$\Rightarrow \dfrac{0.204\times 1000}{1000}$
On simplifying, we get:
$\Rightarrow \dfrac{204}{1000}$
The term can be written as:
$\Rightarrow \dfrac{51\times 4}{250\times 4}$
On simplifying, we get:
$\Rightarrow \dfrac{51}{250}$, which is the required fraction form.

Note: It is to be remembered that we multiplied and divided by $1000$ since there were $3$ decimal places. If there are $n$ decimals, the number should be multiplied and divided by ${{10}^{n}}$. It is to be kept in mind that the value of a fraction does not change when multiplied and divided by the same term.