A percentage is a number or proportion that represents a fraction of 100. It is frequently indicated by the symbol "%" or as "percent" or "pct". For instance, 35% is equal to the decimal 0.35, or the fraction
History of Percentage
In Ancient Rome, well before the presence of the decimal framework, calculations were frequently made in portions, which were products of 1/100. Calculation with these parts was equal to computing percentages. As denominations of cash developed in the Middle Ages, calculations with a denominator of 100 turned out to be progressively standard and from the late fifteenth century to the mid sixteenth century it got regular for math writings to incorporate such calculations. By the seventeenth century it was standard to quote loan costs in hundredths.
Percentage calculations engaged with discovering percentages are not extremely troublesome and any individual without a lot of information about this can do the technique to get results. Individuals frequently need to discover rates, eventually throughout everyday life. Students, teachers, bookkeepers and numerous different professions need to show numbers as percentages.
In spite of the fact that the percentage formula can be written in different forms, it is basically an algebraic comparison involving three values.
P × V1 = V2
P = Representing the percentage
V1 = Value that the percentage will modify
V2 = Being the result
While solving for the percentage, which is to be entered will be the actual percentage and not its decimal representation.
EX: P × 30 = 1.5
This formula requires the percentage to be in the decimal form, so that the solution for P can be simply multiplied by 100 so as to be converted to a percent.
Percentage Change Formula
The increase and decrease in a percentage can be calculated by computing the difference between the two values and comparing it against the initial value. Mathematically, this would mean that we are to find the absolute value of the difference between two values, and then divide the result by the initial value, basically calculating how much the initial value has changed.
This above can be done by first , converting the percent into its decimal form then either subtracting (decrease) or adding (increase) , as per the question demands , the decimal equivalent from and to 1. Multiplication of the original number by this value will give you either an increase or decrease of the number by the given percent. Refer to the example below for clarification.
EX: 500 increased by 10% (0.1)
500 × (1 + 0.1) = 550
500 decreased by 10%
500 × (1 – 0.1) = 450
Percentage Difference Formula
The percentage difference between two units can be calculated simply by dividing the difference between the units, V1 and V2 by the average of those 2 numbers. The resultant is then multiplied with 100 which should give us the percentage.
|Percentage Difference =
|| × 100
1. How to calculate percentage
Percentage value can be calculated by multiplying the numerical value of a ratio on 100. For example, to find 30 oranges percentage of 300 oranges, first, we will calculate a ratio 30/300 = 0,1, and then we multiply 0.1 by 100 to receive 10% as the resultant answer.
To calculate percent from another percent, to convert a certain percentage into shares 100, or decimal, and to increase them.
For example: 400% from 300%:
(400/100) × (300/100) = 40 × 30 = 1200 = 1200/100 = 12%.
There are various formulas available for percentage problems. The most basic formula being X/Y = P x 100. The below given equations are all different version of this formula.
Let's explore the three basic percentage problems , where X and Y represent the numbers and P represents the percentage:
- Find the P percent of X
- Find what percent of X is Y
- Find X when P percent of it is Y
2. How to calculate percentage of a number
Use this percentage formula: P% * X = Y
Example: What is 10% of 150?
- Convert this into an equation using the percentage formula: P% * X = Y
- P is 10%, X = 150, so the equation becomes 10% * 150 = Y
- Convert this 10% into a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10
- Substituting 0.10 for 10% in this equation: 10% * 150 = Y becomes 0.10 * 150 = Y
0.10 * 150 = 15
Y = 15
So 10% of 150 is 15
- Double check your resultant value with the original question: What is 10% of 150?
Multiply 0.10 * 150 = 15
3. How do we find what percentage of X is Y
Use the percentage formula: Y/X = P%
Example: What percent of 60 is 12?
- Convert this into an equation using the percentage formula: Y/X = P%
X is 60,
Y = 12, this implies, 12/60 = P%
Which implies 12/60 = 0.20
- Important! The result which you get will always be in decimal form, not percentage form. multiply the result by 100 to change it into percentage.
Converting 0.20 into percentage : 0.20 * 100 = 20%
So 20% of 60 is 12.
Double check your resultant with the original question: What percentage of 60 is 12?
We get, 12/60 = 0.20, and multiply it by 100 to get percentage, 0.20 * 100 = 20%
4. How do we find X if P percentage of it is Y
Use the percentage formula Y/P% = X
Example: 25 is 20% of what number?
- Convert this into an equation using the percentage formula: Y/P% = X
Y is 25
P% = 20, so this make the equation as 25/20% = X
- Convert this percentage to a decimal by dividing by 100.
Converting : 20/100 = 0.20
Substituting 0.20 for 20% in the equation: 25/0.20 = X
Which implies 25/0.20 = X
X = 125, So 25 is 20% of 125
Double check your resultant with the original question: 25 is 20% of what number?
25/0.20 = 125
5. How Can we convert percentage to decimal
We first remove the percentage sign and then divide the number by 100
EXAMPLE: 15.0% = 15./100 = 0.150
6. How can we convert a decimal to a percentage
Multiply by 100 and add a percentage sign to the number
EXAMPLE: 0.86 = 0.86 * 100 = 86.0%
It not correct to divide a number by 100 and to use a Percent sign all at the same time.
For example: 12% = 12/100 = 0,12, instead of 12% / 100, which actually (12/100)/100 = 0,0012. The term such as (100/100) % is wrong, it can be read as (1) Percent even if the purpose consists to tell 100%. )
Every time when we speak or deal with percent, it is important to specify that it is relative, i.e. that is the general that there correspond 100%.
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