Question

How do you write $\dfrac{13}{20}$ as a decimal and a percent?

Answer 1

Hint: Here we have to convert the given fraction value in decimal and percent. So as we know fraction is converted into decimal by dividing the numerator by the denominator so we will use this method. Then for writing the fraction into percent we will multiply and divide the fraction by $100$ and then by using the definition of percentage get our desired answer.

Complete step-by-step solution:
We have to write the below fraction into decimal and percent form:
$\dfrac{13}{20}$….$\left( 1 \right)$
For converting the fraction into decimal firstly we will make the denominator equal to \[100\] as it is easy to divide a fraction with denominator $100$
So multiply and divide equation (1) by $5$ as below:
$\Rightarrow \dfrac{13}{20}=\dfrac{13}{20}\times \dfrac{5}{5}$
$\Rightarrow \dfrac{13}{20}=\dfrac{65}{100}$
We can rewrite the above value by in decimal form as
$\Rightarrow \dfrac{13}{20}=0.65$
So we can write $\dfrac{13}{20}$ as $0.65$ in decimal.
Next we will write the fraction $\dfrac{13}{20}$ in percent form by multiplying and dividing it by $100$ as follows:
$= \dfrac{13}{20}\times \dfrac{100}{100}$
$= \left( \dfrac{13}{20}\times 100 \right)\times \dfrac{1}{100}$
Now from the definition of percentage we know $\dfrac{1}{100}=1\%$
$= 65\times 1\%$
$= 65\%$
So we can write $\dfrac{13}{25}$ as $65\%$ in percent.
Hence we can write $\dfrac{13}{20}$ as $0.65$ in decimal and $65\%$ in percent.

Note: Fraction is defined as the part of a whole. This whole can be any specific value or a thing. We can simplify the fraction given to convert it into decimal but as it may take a little more calculation we made the denominator $100$ so as to simply move the decimal sign two points towards the left of the number. Percentage is any number or ratio that can be expressed as a fraction of $100$ . Multiplying and dividing by the same number is the same as multiplying by $1$ as we can see in the question that $\dfrac{5}{5}=1$ .