Question

How do you write $300\mathrm{\%}$ as a fraction in simplest form and as a decimal?

Answer 1

Hint: In this problem, we have to convert the given percentage $300\mathrm{\%}$ into its fraction in simplest form and as a decimal. We know that we can write percentage form in another way, that is we can remove the percentage symbol and divide the given number by 100.then we can further simplify the number which is divided by 100 into its simplest form using multiplication tables, and then we will convert into the decimal.

Complete step by step answer:
We know that the given percentage to be converted into a fraction in simplest form is
$\Rightarrow 300\mathrm{\%}$
We can now write the given percentage into its fraction form, we get
$\Rightarrow 300\mathrm{\%}={\displaystyle \frac{300}{100}}$
Here we have removed the percentage symbol and divided the number by 100 to get a fraction form.
Now we can simplify the above fraction further.
We can split the numerator and the denominator, with the multiples of 100, we know that 300 is multiples of 3 and 100, and 100 is the multiple of 100 and 1.
We get,
$\Rightarrow {\displaystyle \frac{300}{100}}={\displaystyle \frac{3\times 100}{100\times 1}}$
Now we can cancel the similar terms in the above step, we get
$\Rightarrow {\displaystyle \frac{300}{100}}={\displaystyle \frac{3\times 100}{100\times 1}}={\displaystyle \frac{3}{1}}$
Therefore, the simplest form of the fraction of percentage $300\mathrm{\%}$ is ${\displaystyle \frac{3}{1}}$.
Now to convert this in to the decimal we have to divide the numerator with denominator we will get
$\Rightarrow {\displaystyle \frac{3}{1}}=3.0$

Therefore, the decimal form is $\Rightarrow {\displaystyle \frac{3}{1}}=3.0$

Note: students should know that we can write percentage form in another way, that is we can remove the percentage symbol and can divide the given number by 100. Students should know multiplication tables to cancel and solve these types of problems easily.