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If you know *how to calculate the percentage* that helps you to earn a good score on math tests as well as in the real world. It’s an easy way to find out the percentage. In this article, we learn how to calculate the percentage. Before calculating the percentage first of all you have to have a clear idea about it.

Percentage means per cent & “percent” means “per hundred”. In mathematics, percentage means a fraction whose rate is 100 and 100% means the whole. The denominator of the fraction is 100 percent. If there are 200% or 300% that means two or three times of the whole. The word percentage is abbreviated as ‘%’. For example “25%” can be pronounced “twenty-five percent” or “25 percent”. And this 25 percent is 25/100 or 0.25.

## Percentage Definition:

Percentage is a ratio that publishes as a fraction of 100. It is denoted by ‘%’.

Example:

The fractions of 150% is 3/2

And 0.5% = 51/200

13 3/4% = 11/80

## How to find percentage

If we say 40%, that means 40/100= 2/5 (after cancelling). So 40% means 2/5. If you just want to find any percent of something like as 20% of 80 =20/100 × 80 = 16

150% = 150 × 1/100 =3/2 =1.5 (by cancelling)

13 %= 13 × 1/100 = 13/100 = 0.13

**Another example percentage**: Instead of saying “it rained 5 days out of every 100,” we say “it rained 5% of the time.”

## Calculate decimal into percentage

For turning a decimal into a percentage just multiply the decimal by 100.

Example: 0.4 = 0.4 × 100 = 40% [Multiply by 100 to add percentage sign]

Similarly

0.98 = 0.98 × 100 = 98%

0.204 = 0.204 × 100 = 20.4%

## How To Calculate The Percentage decimal into decimal

To convert a percentage to a decimal, just divide by 100 to remove the percentage sign.

E.g. 20% = 20/100 = 1/5 = 0.2

13.05 % = 13.05/100 = 0.1305

**What do you mean by the percentage profit rate? **

Answer: The percentage of profit that is taken for one year on 100 dollars is the percentage of profit.

**Percentage change Formula**

Percentage change = (new value-original value)/ (original value) × 100

**For example: The price of some litchis is increased from 90 to 98. How much the price increased?**

**Solution: Percentage change = (98-90)/90 × 100**

** = 8.89 %**

** **

**Re-write this formula we can write **

Original value = (new value × 100)/(100+ Percentage change )

And

New value = (100+ Percentage change × original value )/100

## Percentage increase or decrease

**Percentage increase**

To calculate the percentage increase we need to follow the steps below:

**Step1:** Find the difference between the two numbers you are comparing.

**Increase = New Number – Original Number**

**Step2: Formula:**

Percentage increase= Increase/ (Original number) ×100

**Note: **

If your answer is negative, it will decrease the percentage.

** **

### Percentage decrease

To calculate the percentage decrease we need to follow the steps below:

** Step1:** Find the difference between the two numbers you are comparing.

**Decrease = Original Number – New Number**

* Step2*: use the following formula

**Percentage decrease= decrease/ (Original number) ×100**

**Note: **

If your answer is negative, it will increase the percentage.

Find the original price of something after the price has increased.

Here you need to find the original amount.

**E.g.** A telephone sells for £68, after a 30% increase in the cost price. Find the cost price.

**Solution**

**Start as 100% of the original amount.**

Cost price = 100%

The selling price is 30% of the cost price.

So the selling price is 100% + 30% = 130% of the cost price.

**We know that**

**The selling price is £68, so 130% = £68.**

**Now determine 1%:**

130% = £68

1% = £68/130

1% = £0.5231

The cost price is 100%, so multiply £0.5231 by 100.

Cost price = 0.5231 × 100 = £52.31.

## Percentage Difference Formula

The percentage difference is equal to the absolute value of the value change, divided by the average of 2, all multiplied by 100. Then we add the percentage sign % to determine the percentage difference.

**Percentage difference = (|Value1-Value2|)/ ((Value1 + Value2)/2) × 100**

**E.g. To find the percentage difference between 10 and 17 is**

**Percentage difference = (| 10 -17 |)/ ((10 + 17)/2) × 100**

** = |-7 |/ (27/2) × 100 **

** = 7/ (27/2) × 100 **

** = 14/ (27) × 100 **

** = 0.519 × 100**

** = 51.9% difference**

**Note that** if we use 10 instead of 17 and 17 instead of 10 we will still have a difference of 51.9%. Because we are calculating the difference between two numbers and not changing from one number to another.

### Percentage Error

Percentage error is a special case. Percentage errors are calculated from the perfect change between experimental (measured) and theoretical (recognized) values, and the percentage of relative change is divided by a percentage, especially theoretical (recognized) values.

**Percentage (%) error = (|Experimental-Theoretical|)/ (| Theoretical |) × 100**

** **

### Percentage Error Example

Smith measures the length of her stick as 30cm. If the actual length is 27.9cm, then what is the percentage error in Smith’s calculation?

% error = (|30-27.9 |)/ (|27.9|) × 100

= 2.1/ (27.9) × 100

= 0.0753 × 100

= 7.53%

### Calculating the percentage of a number

**What is 20% of 140?**

To find the value of 20% of 140, we have to multiply 20% by 140. For this, we have to convert 20% to decimal by removing the percentage sign and dividing by 100.

**Solution:** 20% of 140 = 20% × 140

= 20/100 ×140

= 1/5 ×140

= 28

So 20% of 140 is 28

### Calculating the percentage of two numbers

What percent of X is Y? Or what percent of Y is X?

To do this we need to follow the formula below:

Formula Y/X = P%

What percent of 40 is 8?

**Solution: ** Here X= 40

Y= 8

Then, 8/40 = P%

Here 8/40 = 0.2

Note: Results will always come in decimal form, not in percentage form. So you have to multiply the decimal result by 100 to get the percentage.

So conversion of 0.2 to percent is 0.2 × 100 = 20%

Therefore 20% of 40 is 8.

**If the percentage of P is Y then how to find X.**

For this, we use the previous formula Y/X = P%

**We can write it Formula Y/ (P %) = X. Now by placing the given value, we can easily find out the value X. Let’s look at an example.**

**Question: 45 is 15% of what number?**

**Solution: Formula Y/ (P %) = X. **

** 45/ (15%) =X**

** 45/ (15/100) =X**

** (45×100)/15 = X.**

** 300 = X**

**So, X = 300**

**Therefore 45 is 15% of 300**

### Percentage uses:

We use it in almost every aspect of our lives. And it’s also important in our day to day life. Another thing to use percentages is it can be compared easily than fractions

- To find out the nutritional content of food.
- Restaurants using percentage for calculating tips.
- Shops promote discounts on products. These discounts are called percentages. “Up to 60% offer marked prices”.
- Determining statistics.
- As a percentage of money is invested by interest.
- Firms define their achievement or failure as an increase or decrease in profit levels. E.g. “B-Firm profit downcast by 25% for the previous economic year”.
- Calculating Discounts.