Percentages are very important in the study of mathematical concepts and other disciplines such as finance and business sectors. The concept of percentage plays a key role in making useful insights and decisions from the given data as well as everyday calculations and financial analysis.
It is a usual and very common concept in discounts and sales purchases to poll results and weather forecasts. Percentages play a significant role in apprehending and communicating proportions and making them a useful part of calculations while interpreting and managing data.
In this article, we will address the concept of percentages. We will explore its definition with its classifications. We also elaborate on the useful applications of percentages with solved examples.
What are Percentages?
The word percent has been derived from the famous Latin word per centum which means for each hundred. A percentage signifies the portion out of every 100 units. It is frequently represented using the symbol of % and is employed to express the part of the whole as a fraction of 100.
A percentage represents a certain proportion from each 100. The term percentage indicates ratios that are expressed as a part of every 100. e.g. 42% denotes 42 out of every 100 units and 73 % represents 73 out of every hundred which is equivalent to 73/100 or 0.73.
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Percentages can be changed into the form of fractions or decimals as well. For the purpose of converting percentages into fractions, we divide the value given in percentage by a numerical value of 100 and simplify to get the required answer such as 40% = 40/100 = 2/5. On the other side to get answers in the form of decimals, we remove the sign of percentage and then divide this value by 100 such as 85% = 85/100 = 0.85.
Classifications of Percentages:
The term percentage can be categorized into the following forms:
Simple Percentage:
This is the most straightforward form of the percentage and it represents the direct proportion of a whole in the percentage. It is used for basic calculations such as 35% of 60 is 21. Or if you have 25% of a pizza, it implies you have 25 slices from every 100.
Compound Percentage:
This form of the percentage involves multiple computations and this kind of percentage plays an important role in the calculations of problems like compound interests.
Percent of Total:
This kind of percentage denotes the proportion of a part relative to the entire whole part. e.g. In a class of 100 students, 30% of the students are female if 30 of them are females.
Percent Increase or Decrease:
In this form of the percentage, the change in a value is represented as a percentage of the original value. For example, a product has had a 10% price rise if its initial $100 price increases by $10. In the same case, a
20% rise from 100 to 20 gives a new value of 120. Similar to this, a 15% drop in 80 is 12 and gives a new value of 68.
Percentage Error:
Percentage error elaborates on the deviation between the observed value and the expected value which is sometimes also termed the true value. It is represented as the percentage of the expected value. For example, a measurement has a 3.85% error if it is listed or noted as 12.5 cm while the actual measurement is 13 cm.
Percentage Points:
The percentage points signify and compare the numerical difference or magnitude by representing the absolute deviation among the percentages. A rise of 10 percentage points is expressed as an increase from 20% to 30%. Similarly, in the event that an exam’s rate of success improves from 70% to 80%, there is a 10% increase in points of percentage.
Percentage Change:
Percentage change describes the difference as a percentage of the original value and indicates the relative change between percentages. A climb from 20% to 30% corresponds to a 50% rise or increase if the change of 10% is half of the original value of 20%.
Relative Percentage:
Relative percentages demonstrate how different parts of a whole relate to one another proportionally. In a class with 40% female students and 30% male students, the female-to-male student ratio is 4:3.
Examples:
Below are a few examples to learn how to calculate percentage.
Example 1:
Suppose you have a bag containing 3 kg of guava and 5 kg of mangoes. What will be the percentage of the quantities present in the bag?
Solution:
Step 1: Given information:
Guava: 3 kg, mangoes: 5 kg, and total: 8 kg
Step 2: By the definition of the percentage a percentage signifies the portion out of every 100 units. So,
% age of guava = (3/8) x 100 = 37.5 %
% age of mangoes = (5/8) x 100 = 62.5 %
Example 2:
What will be the actual number if 28 % of 60 % of a number is 30?
Solution:
Step 1: Given information:
28 % of 60 % of a number is 30
Step 2: Suppose m is the actual number.
Step 3: According to the given condition:
(28/100) x (60/100) x m = 30
m = (30 x 100 x 100) / (28 x 60)
m = (300,000/ 1680)
m = 179
Applications of Percentages:
Now we will discuss here useful applications of the concept of percentages.
Mathematics and Science:
The concept of percentages is very useful in the study of mathematics and other science disciplines for data analysis and the interpretation of useful insights. They are employed to elaborate on the probabilities in statistical analysis and compare the important results obtained from the given data.
Finance and Economics:
In finance and economics sectors percentages are very important to financial transactions, interest rates, profit margins, and tax computations. They are essential for analyzing investment returns, working out spending plans, and coming to smart financial judgments.
Percentages in Business:
In the business sector, percentages play a key role in understanding sales figures and have an impact on marketing strategy. Understanding such factors is crucial for businesses aiming to achieve success in highly competitive marketplaces.
Wrap Up
In this article, we elaborated on the concept of the percentages. We have explored its definitions in different ways and we have classified them in detail. We have discussed its useful applications in different disciplines with its examples as well.
Hopefully, by reading and apprehending this article you will be able to tackle the problems of percentages in different sectors. It will also enable you to make informed decisions in various aspects of their lives from managing finances to interpreting data.
