Concept of Percentage

The basic concept of percentage in mathematics is used as a ratio or fractional value of 100. In this regard, the overview of percentage, and the definition of percentages provides the overall function of percentage and their application as well. 

Overview of the basic concept of percentage 

Percentage in general terms is considered as a part, portion or share in a whole proportion. The use of percentage first occurred in the mid-1600s, where it was developed by the ancient Roman and Italian mathematicians. In Italy, various abbreviations are used for percentage such as ‘per 100’, ‘p 100’, ‘p cento’ and so on. Additionally, the Latin phrase word ‘per centum’ means ‘for each hundred’ where it was used as ‘o o’ and later on, in modern days it evolved into a ‘%’ symbol. This can be simplified as 1 per cent tells that 1 per 100 or cent. This can be written as 1%, where the concept of numerator and denominator comes first. The percentage is considered an important part of arithmetic as well as statistics. 

Definition of percentage 

The percentage is defined as a portion or number which is mentioned as a quantity out of a hundred. For Instance, it can be said that 1% means, 1 out of 100 or 1/100, but in this regard, 1% per cent of something, for say 1000; means 1/100 of 1000. This turned out as (1/100*1000) =10 per cent. Similarly, 15% of 200, is considered as the (15/100*200) = 30, therefore 15% out of 200 is 30. The percentage also can be written as in terms of decimal, fraction and ratio. 

Function and application of percentages 

Percentage helps to measure a difference from one component to another or to state a fact of a portion by benchmarking an initial value, which is used as 100. For instance, stating a fact that the price of petrol increased 2%, where the benchmark value is the country’s initial price, e.g 100, this means the price increased up to 102. 

A simple formula of percentage

In general, for computing a value (x) as a percentage of another value (y), it can be used as 

[x/y*100%]

In this regard, it can say that 2 (x) as a percentage of 6 (y) can be stated as (2/6*100%) =33.33%

Percentage as fraction

Fractions can convert into percentages and vice versa by multiplying the fraction by 100 and dividing a percentage into fractions. For instance, 3/4 can be written as 3/4 *100= 75%, or 75% means 75/100= 3/4

Percentage as ratio

A simple percentage can be turned into a ratio for instance 75% means = 75/100 or 75:100, where the simplified value will be 3:4. 

Percentage as decimal

50% can be written as 0.50 and vice versa for example 2.50= 250%. 

Percentage mostly used in all types of financial areas and departments as a purpose of everyday usage. For instance, bank interest rates, discounts in various shops, inflation rates and other statistical media as well. 

Increases and decrease of percentages 

One of the most useful applications of percentage is using its increasing and decreasing rate, as it is used in almost every percentage action area. This application is used to measure the increasing and decreasing rate of any elements regarding a base value such as to measure the increasing rate in salary, decreasing rate in petrol price, increasing rate in stock market etc. 

Increased value

The increased value defines as if a certain value for example x, increased up to y%, then the increased value will be [(100+y) % of x]

For example, A person’s salary was 100, which increased up to 5%, then his salary will be {(100+5) % of100} =105 

Vice versa, the person’s salary increased from 100(x) to 105(y), then the percentage of increase in his salary will be (y-x/ x) *100

Or, (increased value/original value) *100

therefore, (5/100) *100= 5%

Decreased value

The decrease concept is the same and the opposite formula of increased value, for example, the salary decreased by 5%. Therefore, {(100-5) % of100} =95 

Compound percentage 

Compound percentages are consequences of increased and decreased percentages, for example, a population increase or to examine the result of depreciation. The present value is x, and some years it increased or decreased up to q%, therefore the value after ‘s’ years, will be-

 x of (1+q/100) s

Additionally, the value of population or depreciation rate of s years ago will be-