Question

How do you convert $5\% $ into a fraction and decimal?

Answer 1

Hint:
Here we need to know that if we are given the term $n\% $ then it can be denoted in the form of fraction as $\dfrac{n}{{100}}$ and now we can convert this fraction into the decimal as we know that when we divide any number with ${10^n}$ we only need to shift the decimal from right to left in the numerator before the $n{\text{th}}$ term from the right.

Complete step by step solution:
Here we are given the percentage which we need to convert into the fraction and decimal. So let us firstly convert it into the fraction form. We need to know that when we are given the number with the percent like $n\% $ we can write it as $\dfrac{n}{{100}}$ in the fraction as percentage is calculated always with respect to $100$
So we can write $5\% = \dfrac{5}{{100}}$
Now we have got the fraction form of the $5\% $ and now we can write it in the form of the decimal. For this we need to know that when we divide any number with ${10^n}$ we only need to shift the decimal from right to left in the numerator before the $n{\text{th}}$ term from the right.
As we have got the fraction $\dfrac{5}{{100}}$ in which we can see that $5{\text{ and 100}}$ are the factor of $5$ so we can cancel them and get the simplified form as $\dfrac{1}{{20}}$
Now if we compare ${10^n}$ with the denominator that is $100 = {10^2}$ we will get $n = 2$
Now we need to shift the decimal in the numerator from the position where it is now towards the left $2$ terms.
Now we know that in the numerator which is $5$ the decimal point is not there but we can insert it and write it as $5.0$ and now we can move the decimal position two times from right to left.
We can write:
$5.0 = 005.0$
Now we will get:
$\dfrac{5}{{100}} = \dfrac{{005.0}}{{100}} = 0.05$
So we can write $5\% = 0.05$ in the decimal form.

Note:
Here the student must remember that whenever we need to convert fraction with the denominator as ${10^n}$ where $n \in Z,n > 0$into a decimal, we just need to shift the decimal in the numerator from right to left till $n$ terms.