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etalon-calculator-screen-3jpg lightmachinery releases third generation of online optical design software john hunter building-expansion-2011-2jpg In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number (pure number).
For example, 45% (read as "forty-five percent") is equal to ^{45}⁄_{100}, 45:100, or 0.45. Percentages are often used to express a proportionate part of a total.
(Similarly, one can express a number as a fraction of 1,000 using the term "per mille" or the symbol "‰".)
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In Ancient Rome, long before the existence of the decimal system, computations were often made in fractions which were multiples of ^{1}⁄_{100}. For example, Augustus levied a tax of ^{1}⁄_{100} on goods sold at auction known as centesima rerum venalium. Computation with these fractions was equivalent to computing percentages.
As denominations of money grew in the Middle Ages, computations with a denominator of 100 became more standard and from the late 15th century to the early 16th century it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three. By the 17th century it was standard to quote interest rates in hundredths.
The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first compute the ratio ^{50}⁄_{1250} = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = ^{25}⁄_{100} = 0.25, not ^{25%}⁄_{100}, which actually is ^{25}⁄_{100}/100 = 0.0025. A term such as ^{100}⁄_{100}% would also be incorrect, this would be read as 1 percent even if the intent was to say 100%.)
Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.
We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that ^{60}⁄_{100} × ^{5}⁄_{100} = ^{3}⁄_{100} or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer: ^{3%}⁄_{10%} = ^{30}⁄_{100} or 30% of all computer science majors are female.
This example is closely related to the concept of conditional probability.
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Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%).
Some other examples of percent changes:
In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, 1 + 0.01x times the original amount).
The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first compute the ratio ^{50}⁄_{1250} = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
^{50}⁄_{100} × ^{40}⁄_{100} = 0.50 × 0.40 = 0.20 = ^{20}⁄_{100} = 20%.
It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% = ^{25}⁄_{100} = 0.25, not ^{25%}⁄_{100}, which actually is ^{25}⁄_{100}/100 = 0.0025. A term such as ^{100}⁄_{100}% would also be incorrect, this would be read as 1 percent even if the intent was to say 100%.)
Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.
In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?
We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that ^{60}⁄_{100} × ^{5}⁄_{100} = ^{3}⁄_{100} or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer: ^{3%}⁄_{10%} = ^{30}⁄_{100} or 30% of all computer science majors are female.
This example is closely related to the concept of conditional probability.
Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%).
Some other examples of percent changes:
In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, 1 + 0.01x times the original amount).
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), the final price will be $198, not the original price of $200. The reason for the 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}); thus 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 xpercent 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 you do not have the same percent change. If the initial percent change is x and the second percent change is y, and the initial amount was p, 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".
Main article: Percent sign
In British English, percent is usually written as two words (per cent), although percentage and percentile are written as one word. In American English, percent is the most common variant(but per mille is written as two words).
In the early 20th century, there was a dotted abbreviation form "per cent.", as opposed to "per cent". The form "per cent." is still in use in the highly formal language found in certain documents like commercial loan agreements (particularly those subject to, or inspired by, common law), as well as in the Hansard transcripts of British Parliamentary proceedings. The term has been attributed to Latin per centum. The concept of considering values as parts of a hundred is originally Greek. The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento. In some other languages, the form procent or prosent is used instead. Some languages use both a word derived from percent and an expression in that language meaning the same thing, e.g. Romanian procent and la sută (thus, 10% can be read or sometimes written ten for [each] hundred, similarly with the English one out of ten). Other abbreviations are rarer, but sometimes seen.
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.
In line with common English practice, style guides—such as The Chicago Manual of Style—generally state that the number and percent sign are written without any space in betweenHowever, the International System of Units and the ISO 31-0 standard require a space
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 is also used to express composition of a mixture by mass percent and mole percent.
Find a percentage or work out the percentage given numbers and percent values. Use percent formulas to figure out percentages and unknowns in equations.
There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.
Let's explore the three basic percentage problems. X and Y are numbers and P is the percentage:
Read on to learn more about how to figure percentages.
Example: What is 10% of 150?
Example: What percent of 60 is 12?
Example: 25 is 20% of what number?
There are nine variations on the three basic problems involving percentages. See if you can match your problem to one of the samples below. The problem formats match the input fields in the calculator above. Formulas and examples are included.
A percentage (%) is a fraction expressed as a part of one hundred, instead of any other denominator. The word comes from the Latin per cent, meaning ‘out of one hundred’.
A half, therefore, is 50%, because 50 is half of 100.
The advantage of working with percentages is that they are relatively straightforward to calculate because, unlike fractions, you are always working with a base of 100.
This page explains how to calculate percentages, and provides some simple percentage calculators for you to use.
Percentages are actually fractions, with a denominator (the number below the line) of 100.
What this means in practice is that you don’t need to worry about whether the numerator (top) divides by the denominator (bottom), or whether it is reduced to its lowest form, as you do when you are working with fractions.
It is simply a matter of working out how many hundredths you have, and then expressing it as a decimal if necessary.
Three types of expression
There are three types of percentage calculations:
We will look at each of these in turn, providing examples of how to calculate them for you to practise, using the percentage calculators on the page if you wish.
What is 10% of 50?
There are two ways to approach this. The first says “I know that 10 is one-tenth of 100. I will therefore divide 50 by 10. The answer is 5”.
This is fine when the numbers are relatively simple. But suppose the numbers are more complicated.
What is 22% of 46?
Now it’s much less straightforward. You can’t just work out what 22% is, expressed as a fraction, and anyway, it’s not a simple fraction.
Instead, you have to divide 46 into 100 equal parts, and work out what 22 of them would be when added together.
So:
46 ÷ 100 = 0.46 [remember, when you divide by 100, you move the decimal point two places to the left].
0.46 × 22 = 10.12
Answer: 22% of 46 is 10.12.
The same rules apply to questions which are written in the form of problems.
You are buying some paint and the shop’s prices do not include VAT [sales tax]. You want to know how much you will be paying in tax. VAT is charged at 20%. The paint costs £15 per pot, and you will need three pots.
The total price of the paint is £15 × 3 = £45.
Effectively, you are being asked ‘What is 20% of £45?’
45 ÷ 100 = 0.45
0.45 × 20 = £9.
Answer: The total tax payable on the transaction will be £9.
Think of this as turning a fraction into a percentage. Your fraction is ^{x}/_{y}, and your percentage is [unknown, here] ^{A}/_{100}.
^{x}/_{y} = ^{A}/_{100}
The easiest way to do these, then, is to move the fraction around. If you multiply both sides by 100, you get A (your unknown) = 100x divided by y. Just plug in the numbers and out will come the answer. Some examples may make this even clearer.
What is 10 as a percent of 50?
Using the formula that we have just worked out, x is 10 and y is 50. The sum is therefore:
100 × 10 = 1000
1000 ÷ 50 = 20.
Answer: 10 is 20% of 50.
This method, of course, also works with a more word-based problem.
You have been quoted commission of $7.50 on the sale of a table. The sale price is $150. Another company has quoted you commission of 4.5%. You want to know which is better value.
This is asking you ‘What is $7.50 as a percent of $150?’.
Using the formula, therefore, x is 7.5 and y is 150.
7.5 × 100 = 750
750 ÷ 150 = 5.
Answer: The commission is 5% on the sale price. The commission of 4.5% is therefore better value for you as a customer.
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fpl calculator enter income here above income is wkly mthly yrly family size including yourself living in alaska hawaii your yearly income is
percent alcohol conversion calculator enter an alcohol percentage in either percent alcohol by volume or percent alcohol by weight and click calculate to see
bonus pay calculator percentage method this bonus pay calculator uses supplemental tax rates to calculate withholding on special wage payments such as
the key thing to remember for doing math for flexible layouts is target context result enter a context width and some target widths to get percentages
when an asset loses value by an annual percentage it is known as declining balance depreciation
bonus percent calculator general information check date state alabama alaska arizona arkansas california colorado connecticut delaware florida
s the percent complete calculated if there are multiple tasks with time frames which all roll up into a high level task for example see
percentage change calculator is a mathematical tool to calculate the relative change to the whole of a given number in percentage the percentage change is
description quickly what s 10 of your lunch tab how about what percentage of 255 68 is use this versatile percentage calculator to ensure you have the
download percentage calculator for android now from softonic 100 safe and virus free more than 303 downloads this month download percentage
how to work out percentages see how by using our percentage calculator online
soil texture calculator download excel version xlsm 155 kb percent sand very coarse sand coarse very fine sand percent clay graph color
for each mark in the view a percent from table calculation computes a value as a percentage of some other value 8212 typically as a percentage of the previous
o calculate percentages is easier than you think quick what s 36 of 25 or how about 250 of 20 learn a quick and dirty tip to help
here are suggested percentage guidelines based on net income compiled by dave ramsey author of financial peace viking 1997 21 95 which he says are
-of-sale systems can easily complete all calculations however there are times when retailers will need to use the percent increase formula
a cgpa calculator to convert your grades and grade points to percentage online using a cce conversion formula by cbse for class 9 class 10 amp class 12th
also enter the percent alcohol by volume alc vol for the alcohol ingredients calculators for beer and wine drink sizes alcohol calories and spending and
debt-to-income calculator help the debt-to-income ratio dti is expressed as a percentage and is your total quot minimum quot monthly debt divided by your gross
my calculator has a percent key i thought that using it to add sales tax to a number would yield the correct total but it gives me a higher amount
the weight loss percentage calculator measures the change in your weight as a percentage rather than as a raw number
use these online calculators to compute exactly how steep that big hill is or how fast or slow you averaged on your last ride and more grade pitch
the samsung galaxy s7 calculator can t do easy percent calculation anymore what to do we tell you a workaround to use the easy percent calculation again
excel percentage calculator - simple excel template to calculate percentage change or percentage as a proportion
illustration 1 adding percentages by multiplication by a decimal ask students to use a calculator with a percentage key to work out how to calculate the
mple calculator to calculate percents it supports the following functions 1 calculate percents and percentages 2 percent discounts sale
the 8220 ingredient percentage calculator 8221 will determine the exact amounts that you ll need of each of your ingredients based on your batch size
by colin beveridge when you re reduced to working on paper on a numeracy test you need to know some techniques for quickly dealing with percentage
percent calculator what is of answer or is what percent of answer if you are no member yet please fill registration form basic fee aed 1000 - or
if you want to combine two feeds with different protein percentages to achieve a protein level in between the two percentages use the following calculator
when writing a formula the easiest method is to do so using what is known as baker s percentage or baker s math in using baker s percentage each ingredient
online molarity calculator from sigma-aldrich com makes calculating molarity and normality for how is the molarity of a percentage solution calculated
heap-percent - calculator for a heap size percentage based on the system ram and a range
fpl calculator please round to the nearest whole number gross household monthly biweekly weekly family size in persons calculate percent of fpl
disclaimer use the child support calculator to get an idea of how much a the law states that the basic support award be set at a fixed percentage of
nline calculator that tells you what percentile your household your household income is your percentile give or take seven percent
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i m very new to domo and am not finding any information on a calculation i want to do i want to show a percent of one item to another on a
for use change the numbers and click on question mark a click on oxygen calculates oxygen click on saturation calculates saturation click on altitude shows
nt error or percentage error is the difference between an here is how to calculate percent error with an example calculation
with the hotforex risk percentage calculator you can easily calculate your lot size by specifying the amount percentage of your balance that you are prepared
the operating profit percentage ratio compares sales to operating profit it will tell you the percentage of your sales that turn into profit
efinition the markup percentage calculation is cost x markup percentage and then add that to the original unit cost to arrive at the sales
automatic percentage equivalent number calculator for increase and percent decrease ratios education or school homework math tool to workout
comprehensive mortgage calculator as well as the basic mortgage calc you depending on the price of the property and percentage of its value you need to
a simple weight loss percentage calculator surrounded by wisdom from dr halls interrupted by the moose because it s fun and interesting
love calculator to calculate compatibility between people this true love meter finds love percentage accurately online love tester game
discover the top 100 best percent calculator apps for ios free and paid top ios apps for percent calculator in appcrawlr
ercent daily value dv found in a nutrition facts table can help if you would like to do your own calculation use the equation below to
dna rna gc content calculator draw gc online please paste the dna rna sequence gc content dna length bp
you can use this low interest or zero percent car loan calculator to figure out your monthly savings if you were to be offered this type of financing option on a new
scroll down to see the uptime calculator you have two options either type in how long website down or type in the uptime percentage
example if you had 20 apples and you gave 5 to your friends how much did you give percentage wise by performing a simple calculation
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