1 June 2023

Throughout history, it has been conceived the idea of ​​percentage. From the implementation of the payment of taxes in ancient Rome by the emperor Augustus until the fifteenth century when it began to be used as a measure to collect interest or taxes. Today, the percentage is a fundamental measure not only in the economy, but also in people’s daily lives.

It is commonly used to calculate the percentage or relative frequency of events, or characteristics in different contexts. From the analysis of surveys and market studies, to the measurement of results in fields such as education and health. In this article will be exposed important aspects about the percentage and its application in the calculation of percentage or relative frequency.

## definition of percentage

For mathematics and statistics it is defined as the expression of a specific amount of a fraction of 100 portions equal. It indicates a proportion and, accompanied by a number, indicates the hundredth part of that amount.

The introduction of the term percentage made it possible to simplify the difficulty of fractions. Well, it is easier to mention 25% than 1 ⁄ 4. Although you can also define the fraction that has 100 in the denominator. The symbol has evolved with the passing of time. In the fifteenth century it was a p rested that indicates “P Cento”. It was in the 17th century that it was perfected until it had the one used today (%), which is accompanied by a figure and reads “percent”.

These present three essential components:

• The final amount.
• The part of that data.
• The percent.

There are programs to convert percentage to decimal or vice versa. are represented using pie charts which are useful, since they facilitate interpretation and allow comparisons to be made at a glance. In general they are used to express numerical data of reality. These graphs are built by drawing the radius of a circle, starting from there, they are measured or divided according to the number of angles.

Besides, percentages can be expressed in decimal, for which you only have to move the comma to the left up to two places without placing the percent sign. For example: Convert 45% to decimal. The decimal expression would be 0.45.

## What is the percentage used for in statistics?

Like all science, statistics uses numbers to make sense of it to events that occur in daily life. Through mathematical operations and properties, percentages allow statistics to evaluate value added taxes. It works to express discounts, offers and promotions in stores. They also serve to compare the rates of illiteracy, population, geometry, surveys, rates of production, mortality, birth. These are accounted for and analyzed through statistics.

## How is the percentage calculated?

There are several ways to calculate the percentage, and absolute and relative frequency can be included in the calculation. One of the most common shapes The way to calculate the percentage is by using the formula and using a calculator.

For calculate the percentage Using the formula, the following steps can be followed:

1. Multiply the number by the desired percentage. For example, to find 10% of 360, multiply 360 by 10% (360 x 10% = 36).
2. Divide the result of the previous operation by 100. This means that you must move the comma two places to the left (36/100 = 0.36).
3. If required, round the figure resulting to the desired number of decimal places.

Another way to calculate the percentage is by using the following formulas:

• Absolute frecuency: (value of interest / total sample) x 100
• Relative frequency: (value of interest / maximum value) x 100

Any of the above methods should give the same result.

Summarizing, it is possible to calculate the percentage using a calculator. To do so, the following steps must be followed:

1. Enter the number you want to find the percentage.
2. Multiply by the desired percentage.
3. Press the percentage key (%). The result will be the percentage of the original number.

For example, if you want to find 4% of 436 using a calculator, you can enter 436, multiply by 4, and then press the percent key. The result will be 17.44, which means that 4% of 436 is 17.44.

## What types of percentages are there?

The types are:

Increment: It is determined by dividing the amount of the increase by the original amount and multiplying by 100.

Example: Luisa earned \$50 and received a salary increase for services rendered at the clinic. From \$30. What percentage did she increase?

Solution:

• Divide \$50 by \$350 (50 ÷350 = 1.66). Obtaining as a result 1.66
• Multiplying 1.66 by 100 gives 166.66%.
• Then it can be deduced that Luisa’s salary was increased by 166.66%

Discount or decrease: The prices are multiplied and divided by 100. Let’s see an example:

In a store they want to reduce the value of a \$30 book by \$5. What percentage of discount will they be applying?

Solution:

• By multiplying 5 x 30 =150
• Divide 150 ÷ ​​100= 15
• Therefore, the percentage applied in the book was 15%

Revenue growth rate: It is obtained by subtracting the income of the first month and the income of the following month. This result is divided by the amount of the first month’s income and multiplied by 100 to convert it to a percentage.

Example: A food company obtains an income in the first month of \$1000 and in the following month the amount was \$3500. What is the value of the growth rate?

Solution:

Income is subtracted (\$3,500-\$1,000=\$2,500). This result is divided by \$1000 (2500 ÷1000= 2.5). The 2.5 is multiplied by 100, obtaining 250.

Therefore, the revenue growth rate was 250%

According to the application of the percentage in the examples, it can be deduced that there are also other types. Between which we have difference and error. The first allows you to compare an old price and a new one. The second is used in the previous when the values ​​are not exact.

## How do you use the rule of three to get percentage?

The percentages are considered direct proportional relationships. Therefore, if one quantity increases, the other also increases in equal proportion, that is, are directly proportional. As mentioned before, when you multiply or divide any proportion by one number, the other value is multiplied or divided by that same number.

Therefore, the method used to find the percentages is through a direct rule of three. This type of simple or direct rule of three allows the resolution of the unknown. This is the result of multiplying two identified values ​​that are located diagonally. To then be divided by the remaining known figure and thus obtain the value of the unknown. The procedure for calculating the percentage by rule of three is as follows:

Example: From a group of 30 students did not attend class 6. What percentage of absent students are there?

• If 30 students is equal to 100 percent of students, what percentage represent 6 absent students.
• You must multiply 6 students by 100, and the result is divided by 30 students.
• The total result is 20 percent.

As mentioned before, percentages are used in people’s lives because they They allow to express the increase or decrease of the quantities. These values ​​are analyzed and compared using statistical and mathematical methods. To describe a phenomenon or fact. From a label that shows the nutritional indexes or weights to technology. By reflecting the amount of battery, storage and performance of any electronic device. Such as: Computer, Tablet, cell phone, among others.