Question

What is $45\%$ as a fraction, a ratio, and a decimal?

Answer 1

Hint: In this problem, we have to convert the given percentage $45\%$ into its fraction, in ratio 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 a 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 ratio and then to the decimal.

Complete step by step solution:
We know that the given percentage to be converted into a fraction is
$\Rightarrow 45\%$
We can now write the given percentage into its fraction form, we get
$\Rightarrow 45\%=\dfrac{45}{100}$
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 5, we know that 45 is multiples of 9 and 5, and 100 is the multiple of 25 and 4.
We get,
$\Rightarrow \dfrac{45}{100}=\dfrac{9\times 5}{25\times 4}$
$\Rightarrow \dfrac{45}{100}=\dfrac{9\times 5}{5\times 5\times 4}$
Now we can cancel the similar terms in the above step, we get
$\Rightarrow \dfrac{45}{100}=\dfrac{9}{5\times 4}$
$\Rightarrow \dfrac{45}{100}=\dfrac{9}{20}$
Therefore, the simplest form of the fraction of percentage $45\%$ is$\dfrac{9}{20}$.
Now in the form of ratio is
$\Rightarrow 45\%=45:100=9:20$
Now to convert this in to the decimal we have to divide the numerator with denominator we will get
$\Rightarrow \dfrac{9}{20}=0.45$
Therefore, the decimal form of $45\%$ is $\Rightarrow \dfrac{9}{20}=0.45$

Note: Students should know that any form of percentage can be expressed in the fractional form by dividing it by 100. The obtained fraction may or may not be reduced further. If the fractional value can be reduced it must be reduced to the least fractional value by breaking the numerator and denominator into factors and then cancelling the common factors of both.