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342 Calculating percentages can be an easy task. There are numerous percentage calculators online that can help with task by simply searching for a “percentage calculator.” However, there may be a time when (however, unlikely it sounds) you may need to be able to calculate percentages without any digital assistance.

### Calculating Percentage

Before you can calculate a percentage, you should first understand exactly what a percentage is.

The word percentage comes from the word percent. If you split the word percent into its root words, you see “per” and “cent.” Cent is an old European word with French, Latin, and Italian origins meaning “hundred”. So, percent is translated directly to “per hundred.” If you have 87 percent, you literally have 87 per 100. If it snowed 13 times in the last 100 days, it snowed 13 percent of the time.

The numbers that you will be converting into percentages can be given to you in 2 different formats, decimal and fraction. Decimal format is easier to calculate into a percentage. Converting a decimal to a percentage is as simple as multiplying it by 100. To convert .87 to a percent, simply multiple .87 by 100.

.87 × 100=87

If you are given a fraction, convert it to a percentage by dividing the top number by the bottom number. If you are given 13/100, you would divide 13 by 100.

13 ÷ 100 = .13

Then, follow the steps above for converting a decimal to a percent.

.13 × 100 = 13

Thus getting 13%.

The more difficult task comes when you need to know a percentage when you are given numbers that don’t fit so neatly into 100.

Most of the time, you will be given a percentage of a given number. For example, you may know that 40 percent of your paycheck will go to taxes and you want to find out how much money that is. To calculate the percentage of a specific number, you first convert the percentage number to a decimal.

This process is the reverse of what you did earlier. You divide your percentage by 100. So, 40% would be 40 divided by 100 or .40.

40 ÷ 100 = .40

Once you have the decimal version of your percentage, simply multiply it by the given number. In this case, the amount of your paycheck. If your paycheck is \$750, you would multiply 750 by .40.

750 × .40 = 300

Let’s try another example. You need to save 25 percent of your paycheck for the next 6 months to pay for an upcoming vacation. If your paycheck is \$1500, how much should you save?

Start by converting 25 percent to a decimal.

25 ÷ 100 = .25

Now, multiply the decimal by the amount of your paycheck, or 1500.

1500 × .25 = 375

You need to save \$375 from each paycheck.

A percentage is a fraction whose denominator (bottom) is 100. So if we say 50%, we mean 50/100 = 1/2 (after cancelling). So 50% means ½. If want to find 10% of something, ‘of’ just means ‘times’. So 10% of 150 = 10/100 × 150 = 15.

If you have to turn a percentage into a decimal, just divide by 100. For example, 25% = 25/100 = 0.25. To change a decimal into a percentage, multiply by 100. So 0.3 = 0.3 × 100 =30% .

Calculating Percentage Example

Find 25% of 10 (remember ‘of’ means ‘times’).

25/100 × 10

= 2.5

The video below shows you how to handle some exam questions regarding percentage, including: turning decimals into fractions, how to calculate the percentage of a value, calculating percentage change and calculating compound interest.

Calculating Percentage Percentage Change

% change = new value – original value × 100

original value

Example

The price of some apples is increased from 48p to 67p. By how much percent has the price increased by?

% change = 67 – 48 × 100

48

= 39.58%

Percentage Error

% error = error × 100

real value

Example

Nicola measures the length of her textbook as 20cm. If the length is actually 17.6cm, what is the percentage error in Nicola’s calculation?

% error = 20 – 17.6 × 100 = 13.64%

17.6

Original value

Original value = New value × 100

100 + %change

Example

Amish buys a stamp collection and makes a 35% profit by selling it for £2700. Find the cost of the collection. It is the original value we wish to find, so the above formula is used. 2700 × 100 = £2000

100 + 35

Percentage Increases and Interest

New value = 100 + percentage increase × original value

100

Example

£500 is put in a bank where there is 6% per annum interest. Work out the amount in the bank after 1 year.

In other words, the old value is £500 and it has been increased by 6%.

Therefore, new value = 106/100 × 500 = £530 .

Compound Interest

If in this example, the money was left in the bank for another year, the £530 would increase by 6%. The interest, therefore, will be higher than the previous year (6% of £530 is more than 6% of £500). Every year, if the money is left sitting in the bank account, the amount of interest paid would increase each year. This phenomenon is known as compound interest.

The simple way to work out compound interest is to multiply the money that was put in the bank by nm, where n is (100 + percentage increase)/100 and m is the number of years the money is in the bank for, i.e:

(100 + %change)no of years × original value

So if the £500 had been left in the bank for 9 years, the amount would have increased to:

500 × (1.06)9 = £845 Percentage decreases

New value = 100 – percentage decrease × original value

100

Example

At the end of 2003 there were 5000 members of a certain rare breed of animal remaining in the world. It is predicted that their number will decrease by 12% each year. How many will be left at the end of 2005?

At the end of 2004, there will be (100 – 12)/100 × 5000 = 4400

At the end of 2005, there will be 88/100 × 4400 = 3872

The compound interest formula above can also be used for percentage decreases. So after 4 years, the number of animals left would be:

5000 x [(100-12)/100]4 = 2998

### Summary

Hopefully, you will now be able to calculate percentage with ease. Let us know in the comment section if you have any doubts.

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