It is essential to have the ability to convert numbers, fractions and decimals into percentage values, especially in work and in industry, commerce, economics and even engineering. However, it is also very useful in everyday life; We all know how to tip 15%, but how many know how to quickly calculate the amount? Also, being able to describe a quantity as a percentage helps you visualize and account for the amount.
Steps
Method 1 of 3: Evaluate a Percentage Without a Calculator
Step 1. To quickly estimate a percentage, you can use simple addition and subtraction
This technique is very useful when you need to calculate tips or on any occasion when you don't have a calculator available. The percentages can be added and subtracted from each other as long as they express a part of the same unit (e.g. 5% of 8 kg of turkey meat cannot be added to 20% of 3 kg of turkey meat). The technique described here makes it easier to calculate the approximate percentages.
For example, suppose you want to tip 20% of the value of your lunch bill which is € 23.50. With a few simple mathematical tricks you can relatively easily estimate the amount equivalent to 20%
Step 2. Move the decimal point one place to the left and instantly find 10% of the bill
This is the easiest way to get approximate percentages without using a calculator. Basically, you have to move the decimal point one place to the left and you will know that 10% of € 23.50 corresponds to € 2, 35. Remember that at the end of a number there is always a decimal point, even if it is invisible; for this reason you can think of the number 25 as 25.00.
- 10% of 100 is 10.
- 10% of 35.59305 is 3.559305.
- 10% of 6.2 is 0.62.
Step 3. Add and subtract the estimated 10% value to get the figure you want
For example, on a € 23.50 bill you want to tip 20% and not just 10%. Now, since 20% is simply double 10% you can find the right figure by doubling the value you found earlier which is 10%. Consequentially:
- 10% of € 23.50 = 2.35.
- 20% = 10% + 10%.
- 20% = € 2, 35 + € 2, 35.
- A 20% tip on a bill of € 23.50 = € 4, 70.
- This method works because, in practice, percentages are fractions. 10% equals 10/100 and if you add together 10 values that correspond to 10% of a total unit, in the end you will get the unit itself, that is 100%. If you add two values corresponding to 10% you will find the equivalent of 20% and so on.
Step 4. Continue to manipulate the 10% value to estimate other percentages
Once you understand the basic mechanics, you can use them to your advantage to find values corresponding to many other percentages. For example, if the waiter was rude and unhelpful, you could tip him as little as 15%. Break this percentage down into smaller parts and you will find that 15% = 10% + 5%. Since 5 is half of 10, you can find what this is by dividing the estimated value by two. So 15% corresponds to € 2, 35 + € 1, 17; at this point you know that the total tip is € 3.52. Here are some other useful tricks:
- To calculate 1% of a unit, move the decimal point two places to the left. So 1% of 23.5 is 0.235.
- 25% of a number is always its quarter, so just divide the integer by 4.
- 50% of a unit is its half (divide by 2).
- 33% of a value is its third (divide the number by 3).
Method 2 of 3: Converting Fractions to Percentages
Step 1. Remember that percentages are nothing more than fractions with a denominator of 100
All percentages are a way to express cents and let you know how many parts of a set you need to consider if it is made up of 100 servings in all. For example, you can say that 25% of your apple crop is always rotten. In practice, every 100 apples you collect, 25 are to be thrown away, that is 25/100. Conversion to fractions allows you to calculate percentages for real world events; for example, it lets you figure out what your unusable crop percentage is if you have 450 rotten apples out of 2500.
- If your fraction already has the denominator equal to 100, such as 25/100, then the numerator also represents the percentage.
- The writing 1% means "1 in 100".
Step 2. Express a problem described in words in fractions
Sometimes you don't have a fraction available and you have to set it yourself. The hardest part is figuring out which number goes to the numerator and which to the denominator. The number under the fraction sign always represents "the whole". The denominator is the total number of apples you have collected, the value of the restaurant bill, the number of slices that make up a pie, and so on. This is the integer whose percentage you need to calculate. The examples described here show you how to compose fractions:
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Luca has 4000 songs. If 500 are by Vasco Rossi, what is the percentage of songs from the legend of Zocca?
You have to find the percentage of Vasco's songs out of the total of 4000 songs. The fraction will be 500/4000
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Giovanni invested € 1000 in shares. Three months later, he noticed that the prices had risen and now he has € 1342. What is the growth rate of the shares?
Since you are trying to find the percentage of 1000, which has grown, then the fraction is 1342/1000
Step 3. Check if you can easily transform the denominator into the value 100, by multiplying or dividing
If you can "make" the denominator equal to 100 with a few calculations, then the equivalent numerator will also be your percentage and the conversion can be said to be finished. But remember that you must also subject the numerator to whatever mathematical manipulation you decide to subject the denominator. Eg:
- Problem: convert 3/25 to a percentage.
- You can easily turn 25 into 100 because: 4 x 25 = 100.
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Multiply both the numerator and the denominator by 4 and you will find the equivalent fraction: 12/100.
- 4 x 3 = 12.
- 4 x 25 = 100.
- The numerator is your percentage value: 3/25 = 12/100 = 12%.
Step 4. Proceed to divide between numerator and denominator, if you can't easily convert the denominator to 100
For example, in the case of 16/64, it is not easy to transform 64 into 100, so divide the numerator by the denominator. At this point you get: 16: 64 = 0.25.
The quotient is a simple decimal number, but it can be expressed as a fraction that has a larger numerator, as long as we put a larger value in the denominator as well
Step 5. Multiply the obtained value by 100 and convert the decimal value to a centesimal fraction
In the previous example 16/64 = 0.25; then you can proceed to 0.25 x 100 and move the decimal two places to the right getting 16/64 = 25%.
- This final step is identical to the method you already know, when the denominator of a fraction is equal to 100, since 12/100 multiplied by 100 equals 12.
- The decimal point represents, in practice, the percentage of "one". For every 0, 1 you add, you get closer and closer to the unit "1" (0, 9 + 0, 1 = 1, 0). This is why moving the decimal point allows you to turn the number into a percentage, because you can determine how many parts the whole "unit" you are considering is made up of, for example "a" crop of 2566 apples.
Step 6. Try to solve another problem to test your conversion skills
The recommended daily calorie intake is 2000 calories. Today you took in just 2000 calories but, in the evening, you went out and ate an ice cream and a slice of cake that added another 1500 calories. What is the percentage of recommended calories you have consumed today?
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Find the total calories you have eaten.
In this case 2000 + 1500 = 3500 calories
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Set the fraction.
Think "whole". A day's food equals 2000, so you need to find out what percentage of 2000 calories you have eaten. Your fraction will be 3500/2000
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Divide your total calories (3500) by the recommended calories (2000).
3500 ÷ 2000 = 1, 75
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Multiply this value by 100 and get the percentage.
1.75 x 100 = 175
- You took 175% of the recommended daily allowance of calories.
Method 3 of 3: Convert Percentages to Numbers
Step 1. Remember that you cannot use percentages to perform every mathematical calculation
The expression 25% is nothing more than a "shortcut", an easy way to compare two numbers, but it doesn't say much more. For example, by stating that 13% of your 2,566 apple crop is rotten, you don't know exactly how many apples are no longer edible, but 13 out of 100 are to be thrown away. To find the exact number of inedible apples, you need to convert the percentage to a number.
Step 2. Remove the percent sign (%) and move the decimal point two places to the left
In this way you will have a number, usually a decimal, which allows you to proceed with the calculations. If 13% of your apples have rotted, then at the end of this step you will get the number 0, 13.
Moving the decimal point two places to the left is the same as dividing by 100
Step 3. Multiply the decimal value by your integer
In this example you are trying to find how many apples equals 13% of 2566. To find out, multiply 0.13 x 2566. The product will tell you exactly how many apples are rotten, that is 333, 58.
Step 4. Check the calculations with the backward process
To make sure you haven't made a mistake, divide the number of bad apples by 0, 13; the quotient should be 2566. This is the method you must use also to know what is the total number of objects that make up the unit starting from a percentage. For instance:
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Marco owns 20% of all marbles in the class, exactly 10 marbles. How many marbles are there, in total, in the class?
- 20% → 0, 20.
- 10 divided by 0, 20 = 50.
- There are a total of 50 marbles in the class.
Convert to Percentage Step 15 Step 5. Try some practical examples
You found a blouse you like very much for € 50, but today it is discounted by 15%. So what is the final price?
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Convert 15% to decimal value.
15% → 0.15 or 15/100
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Multiply the decimal value by € 50.
0.15 for 50 = € 7.55
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Subtract the found value from the starting price.
€ 50 - €7, 50 = € 42, 50
- You can buy the blouse for € 42.50.
Advice
- A percentage expresses a number as a part of 100. You can think of a percentage as a fraction whose denominator is 100.
- In practice, the conversion to a percentage value results in finding the equivalent fraction with denominator 100 and rewriting only the numerator followed by the percent sign (%).
