Knowing how to calculate a percentage will help you in a math test as well as in everyday life. Percentages are used to calculate tips in restaurants, identify the nutritional content of foods, in statistics and in many other areas. Regardless of the field in which you will try, knowing how to calculate percentages is a fundamental skill that is very simple to acquire.
Steps
Method 1 of 3: Calculate the Percentage of an Integer
Step 1. Graphically view what a percentage represents
A percentage indicates an amount equal to a portion of an integer. A null quantity is represented by 0% while the whole is represented by 100%. Any other value expressed as a percentage is between these two extremes.
- For example, assume you have 10 apples. If you eat 2, it means that you have eaten 20% of your apples (2/10 × 100% = 20%). If the starting 10 apples represent 100% and you have eaten 20%, it means that you still have 80% left (100% - 20% = 80%).
- The term "percentage" derives from the Latin per centum that is "per cent".
The percent symbol is just one of the formats that can be used to express a percentage
In the statistical field, percentages are often expressed as coefficients between 0 and 1, where 1 represents the integer, that is 100%. To obtain the classic format in which the percentages are expressed, simply multiply the decimal coefficient by 100.
Step 2. Determine the percentage value of a quantity of an integer
In some cases you will be provided with two pieces of information: a quantity and the total overall value. In other cases you will be given two values which add up to represent the grand total. It is important to distinguish what the percentage under consideration refers to. For example, assume you have a jar containing 1,199 red marbles and 485 blue marbles, for a total of 1,684 marbles. In this case, 100% of the marbles in the jar is equal to 1,684 units.
Step 3. Find the value you want to express as a percentage
Suppose you want to find the percentage of blue marbles in the jar. In this case you have to find the percentage that represents the value 485 (the number of blue marbles) compared to the number 1,684 (which represents the total, i.e. 100%).
Step 4. Express the two numbers as a fraction
The number indicating a part of the total must be indicated in the numerator of the fraction while the value indicating the total must be indicated in the denominator. In this example we will get 485 / 1.684 (the quantity of which we want to calculate the percentage value divided by the total number).
Step 5. Convert the fraction to a decimal number
Percentages are obtained from the decimal form of a fractional value. To transform the fraction 485 / 1.684 into a decimal number simply perform the calculation using a calculator or a paper and pencil. In the example we will get the decimal number 0, 288.
Step 6. Convert a decimal number to a percentage
Multiply the result obtained in the previous step by the coefficient 100 (hence the name percentage i.e. percent). Following the example above you will get 0.88 × 100 = 28.8%.
• The simplest way to multiply a decimal number by 100 is to move the decimal separator (the comma) towards right of two positions.
• The percentage symbol must be placed to the right of the final result (without leaving blank spaces), exactly as if it were a unit of measurement.
Method 2 of 3: Calculate the Numeric Value of a Percentage
Step 1. Identify the numbers you will need to work on
Suppose you have asked for a loan from a friend to whom a daily interest rate must be applied. The sum he lent to you is € 15 and the daily interest rate is 3%. These are the only data you have available to perform the calculation.
Step 2. Convert the percentage to a decimal number
Perform the reverse procedure of the calculation shown in the previous step of the article, i.e. divide the percentage value by 100 or multiply it by the coefficient 0.01 (the two operations are equivalent). As a result you will get 3/100 = 0.03.
Alternatively, you can simply move the decimal point two places towards left.
Step 3. Reformulate the initial problem using the new values you obtained
It will help you to use the new values obtained and the following formula " X from Y is equal to Z". The term X represents the decimal form of the initial percentage, the preposition" di "indicates the mathematical operation of multiplication, the term" Y "represents the total quantity and the term" Z "is the final result. Replacing each element with the correct values you will get 0, 03 × 15 € = 0, 45 €.
- In this example, the daily interest you will have to pay your friend for the loan he has granted you is € 0.45.
- If you need to calculate the total amount that you will have to repay after "n" days, remember that you will have to add the daily interest multiplied by the total number of days to the initial capital you have borrowed. For example € 15 + (€ 0.45 x 1 day) = € 15.45.
Method 3 of 3: Calculate the Percentage of a Discount
Step 1. Make a note of the starting price and the discount percentage to apply
The original price, normally, is the figure highlighted or written in large by the retailer on the label, so that the "customer" can calculate the discount and understand whether or not it is a good "deal".
Check whether the discount rate should be applied to each individual item purchased or to the final amount
If the discount is applied to the total amount of the purchase, you will have to add the prices of the individual items to obtain the total value to which you will have to apply the discount. Otherwise you will have to apply the discount to the single starting price.
Step 2. Find out what percentage of the starting price you will actually have to pay
This is a trick that allows you to perform only one calculation instead of two. To find out the percentage in question, subtract 100% the discount percentage that is applied, in order to directly obtain the percentage of the original price that you will actually have to pay at the checkout. For example, if you are buying a shirt that is discounted by 30%, it means that you will pay 70% of the original price for it.
Step 3. Convert the percentage to be paid into a decimal number
To do this, divide the percentage by 100, multiply it by 0, 01, or move the decimal point two places towards left. In the example above you will get 70% / 100% = 70/100 = 7/10 = 0, 7.
Step 4. Multiply the starting price by the decimal coefficient you got
If the shirt you want to buy costs € 20, multiply the price by 0, 7. In this case the result is 14, so the final price of the shirt will be € 14.
Step 5. Calculate the discount amount so that you feel more satisfied
Once you have returned home, it can be useful to check the receipts not only to be sure that the discount has been applied correctly, but also to calculate how much money you have saved thanks to it. In this case, you simply have to subtract the amount paid from the original price. In the example above you will get € 20 - € 14 = € 6.
