Question

How do you convert $$20\mathrm{\%}$$ into a fraction in simplest form?

Answer 1

Hint:
A percentage is basically just another form of fraction. However, it is written in a specific format where the bottom number (denominator) is 'fixed' at $100$. It means ${\displaystyle \frac{1}{100}}$. "Percent" or "$\mathrm{\%}$" means "out of $100$" or "per $100$". For example, $x\mathrm{\%}$ can be written as ${\displaystyle \frac{x}{100}}$.

Complete step by step solution:
According to the given information, we have to turn $$20\mathrm{\%}$$into a fractional form.
For that, firstly we need to write the given percentage as fraction by taking 100 as a denominator.
In this case, $$20\mathrm{\%}$$is to be written as $${\displaystyle \frac{20}{100}}$$.
Now the fraction needs to be simplified further,
$$\therefore {\displaystyle \frac{20}{100}}={\displaystyle \frac{2}{10}}={\displaystyle \frac{1}{5}}$$

Therefore, $$20\mathrm{\%}$$ is equivalent to $${\displaystyle \frac{1}{5}}$$ in fractional form.

Additional Information:
In the process of converting percentage into fraction, we need to know that,
1. If $$\mathrm{\%}(<100)$$it will form a proper fraction,
2. If $$\mathrm{\%}(>100)$$ an improper/ mixed fraction will be formed and,
3. If $$\mathrm{\%}$$is in multiples of $$100$$ then the obtained result will be an Integer.

Note:
A percentage is written in a specific format where the bottom number (denominator) is 'fixed' at $100$. To convert the percent into fraction, we need to write the given percentage as fraction by taking $100$ as a denominator and then simplify the given fraction if necessary.