## Percentages and percentage change – concepts and applications

Percent (read as per cent) means ‘every hundred’, or, essentially, ‘out of 100’. If we are given a fraction, we can simply convert it to a percentage by multiplying 100. Say, we have ½, which, when multiplied with 100 becomes ½ x 100 = 50%.

**What do we mean by a percentage change?**

Say, a person has 20 chocolates. If his number of chocolates is increased by 10%, what does it mean? First of all, let us see what is doesn’t mean: after the increase, the number of chocolates with him is NOT 20 + 10 = 30, nor is it 20 + ^{10}/_{100} = 20.1

When we talk of a percent increase, we must understand on what **BASE VALUE** is the percentage change working on. In this case, obviously, the 10% increase is 10% of the number of chocolates he has, i.e. 20. Thus, the number of chocolates with him would become:

20 + 10% of 20 = 20 + 20 x ^{10}/_{100} = 22

Observe that: **20 + 20 x ^{10}/_{100} = 20 x (1 + ^{10}/_{100}) = 20 x (1 + ^{1}/_{10}) = 20 x (^{11}/_{10}) = 20 x 1.1**

Thus, a **10% increase is essentially an increase of ( ^{1}/_{10})^{th} which basically means a multiplication with ^{11}/_{10} or 1.1**; we can use either value depending on the convenience of using a decimal number or using a fraction.

Below is a list of certain percent values and the corresponding number with which to multiple for a corresponding percentage increase or decrease:

We have seen above, that, for a given percentage change, we can calculate the final value. However, if the initial and final values are known, how do we **calculate percentage change**?

** **Percentage change is simply the change in value taken as a percentage of the initial value. Thus:

Note that the ratio of the ‘Final’ and ‘Initial’ values is the same as the number with which we multiply in case of a given percent change (shown in the table above).

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