Percentage is a fraction or a ratio in which the value of whole is always 100. For example, if Sam scored 30% marks in his math test, it means that he scored 30 marks out of 100. It is written as 30/100 in the fraction form and 30:100 in terms of ratio.
Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Calculating percentage means to find the share of a whole, in terms of 100. There are two ways to find a percentage:
1 By using the unitary method.
2 By changing the denominator of the fraction to 100.
It should be noted that the second method for calculating percentage is not used in situations where the denominator is not a factor of 100. For such cases we use the unitary method.
Grammar and style guides often differ as to how percentages are to be written. For instance, it is commonly suggested that the word percent (or per cent) be spelled out in all texts, as in "1 percent" and not "1%". Other guides prefer the word to be written out in humanistic texts, but the symbol to be used in scientific texts. Most guides agree that they always be written with a numeral, as in "5 percent" and not "five percent", the only exception being at the beginning of a sentence: "Ten percent of all writers love style guides." Decimals are also to be used instead of fractions, as in "3.5 percent of the gain" and not "3+1⁄2 percent of the gain". However the titles of bonds issued by governments and other issuers use the fractional form, e.g. "3+1⁄2% Unsecured Loan Stock 2032 Series 2". (When interest rates are very low, the number 0 is included if the interest rate is less than 1%, e.g. "0+3⁄4% Treasury Stock", not "3⁄4% Treasury Stock".) It is also widely accepted to use the percent symbol (%) in tabular and graphic material.
Percent is another name for indicating hundredths. Thus, 1% is one-hundredth, that means 1%=1/100=0.01.
Let's calculate percentage using the two methods given above.
When we have two or more values that add up to 100, then the percentage of those individual values to the total value is that number itself. For example, Sally bought tiles of three different colors for her house
The percentage formula is used to find the share of a whole in terms of 100. Using this formula, you can represent a number as a fraction of 100. If you observe carefully, all the three ways to get percentage shown above can be easily calculated by using the formula given below:
Percentage= (Value/Total Value)×100
The word "percentage" is often a misnomer in the context of sports statistics, when the referenced number is expressed as a decimal proportion, not a percentage: "The Phoenix Suns' Shaquille O'Neal led the NBA with a .609 field goal percentage (FG%) during the 2008–09 season." (O'Neal made 60.9% of his shots, not 0.609%.) Likewise, the winning percentage of a team, the fraction of matches that the club has won, is also usually expressed as a decimal proportion; a team that has a .500 winning percentage has won 50% of their matches. The practice is probably related to the similar way that batting averages are quoted.
As "percent" it is used to describe the steepness of the slope of a road or railway, formula for which is 100 × rise / run which could also be expressed as the tangent of the angle of inclination times 100. This is the ratio of distances a vehicle would advance vertically and horizontally, respectively, when going up- or downhill, expressed in percent.
Percentage difference is the change in the value of a quantity over a period of time in terms of percentage. Sometimes we need to know the increase or decrease in some quantity as percentages, which is also referred to as Percentage Change. For example, an increase in population, a decrease in poverty, and so on.
We have the formula to show the change in quantity as a percentage. There are two cases that might arise while calculating percentage difference and those are:
1 Calculate percentage increase
2 Calculate percentage decrease
Percentage increase refers to the perchange change in the value when it is increased over a period of time. For example, population increase, increase in the number of bacteria on a surface, etc. Percentage increase can be calculated by using the following formula:
Percentage Increase= (Increased Value-Original value)/Original value × 100
Percentage decrease refers to the perchange change in the value when it is decreased over a period of time. For example, decrease in the level of rainfall, decrease in the number of Covid patients, etc. Percentage decrease can be calculated by using the following formula:
Percentage Decrease= (Original value-Decreased Value)/Original Value × 100
Percent changes applied sequentially do not add up in the usual way. For example, if the 10% increase in price considered earlier (on the $200 item, raising its price to $220) is followed by a 10% decrease in the price (a decrease of $22), then the final price will be $198—not the original price of $200. The reason for this apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different quantities ($200 and $220, respectively), and thus do not "cancel out".
In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p(1 + 0.01x)(1 − 0.01x) = p(1 − (0.01x)2); hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number). Thus, in the above example, after an increase and decrease of x = 10 percent, the final amount, $198, was 10% of 10%, or 1%, less than the initial amount of $200. The net change is the same for a decrease of x percent, followed by an increase of x percent; the final amount is p(1 - 0.01x)(1 + 0.01x) = p(1 − (0.01x)2).
This can be expanded for a case where one does not have the same percent change. If the initial amount p leads to a percent change x, and the second percent change is y, then the final amount is p(1 + 0.01x)(1 + 0.01y). To change the above example, after an increase of x = 10 percent and decrease of y = −5 percent, the final amount, $209, is 4.5% more than the initial amount of $200.
As shown above, percent changes can be applied in any order and have the same effect.
In the case of interest rates, a very common but ambiguous way to say that an interest rate rose from 10% per annum to 15% per annum, for example, is to say that the interest rate increased by 5%, which could theoretically mean that it increased from 10% per annum to 10.05% per annum. It is clearer to say that the interest rate increased by 5 percentage points (pp). The same confusion between the different concepts of percent(age) and percentage points can potentially cause a major misunderstanding when journalists report about election results, for example, expressing both new results and differences with earlier results as percentages. For example, if a party obtains 41% of the vote and this is said to be a 2.5% increase, does that mean the earlier result was 40% (since 41 = 40 × (1 + 2.5 / 100 )) or 38.5% (since 41 = 38.5 + 2.5)?
In financial markets, it is common to refer to an increase of one percentage point (e.g. from 3% per annum to 4% per annum) as an increase of "100 basis points".
1 To find the percentage of a whole, work out the value of 1% and then multiply it by the percent we need to find.
2 An increase or decrease in any quantity can be expressed as a percentage.
3 Fractions can be converted into percentages and vice-versa.
4 Percentages are reversible. For example, 25% of 40 is the same as 40% of 25.
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