Question

How do you write $\dfrac{13}{40}$ as a percentage?

Answer 1

Hint: We first define the concept of percentage. We describe the use of the unitary system and the process to get the percentage value from that. We explain the relationship between the ratios and the fractional value for getting the percentage value. To get the percentage, we will simply multiply the given fraction by 100.

Complete step-by-step solution:
The concept of percentage comes from the value of a number being raised to the ratio value of 100 from 1.
The base for the given number is 1 and when that number is multiplied by 100, we get its percentage value.
For example, if we take a number x and try to find its percentage value with respect to the number y, then we have the ratio value of x with respect to y as $\dfrac{x}{y}$. The ratio value is evaluated to get the base of 1.
The percentage value becomes $\dfrac{x}{y}\times 100=\dfrac{100x}{y}$.
For our given fraction $\dfrac{13}{40}$, we need to find its percentage value.
Here we multiply $\dfrac{13}{40}$ with 100 to get the percentage value. The fraction is already with base 1.
So, the percentage value is $\dfrac{13}{40}\times 100=\dfrac{130}{4}=32.5$.
Therefore, we write $\dfrac{13}{40}$ as a percentage value of 32.5.
We can represent it as 32.5%.

Note: We need to remember that for $\dfrac{13}{40}$, the percentage value of 13 is measured with respect to 40. The unitary value is measured when we are taking the base as 1. We can also find the value in decimals by performing the division of 40 by 13. Then, we can multiply the result by 100 to get the percentage.