A percentage is the top part of a fraction whose bottom part is 100.
So 50% means 'half of' and 25% means 'a quarter of'. 100% means the complete quantity.

Why bother with them?

Percentages are useful because they make it very easy to compare things.
For example, suppose the marks in two successive tests are 67/80 and 51/60. It is not very easy to say which of these was best. Percentages use our ordinary number system of 10's, 100's etc and, because they are out of 100 rather than 10, we avoid a lot of the decimal points which make some people twitchy.

Changing a fraction to a %

Taking the example of the test mark of 67 out of 80,

Multiplying both sides of this equation by 100 gives us

Question:- What is the second test mark of 51/60 as a %? Try this yourself before looking. Answer so the mark in the second test was higher.

Changing a % to a fraction

Example:- What is 35% as a fraction?

Remember that the value of a fraction remains unchanged when you multiply or divide both the top and the bottom by the same number.

Changing a decimal to a %

Dead easy, this one!
Suppose we want to write 0.27 as a %. Since a decimal is a kind of fraction, all we have to do is to multiply by 100. You just need to remember that each time you multiply by 10 the number becomes larger by a factor of 10 so the decimal point moves one place to the right. Multiplying by 100 moves it 2 places to the right. This neat rule is because decimals are fractions in our base ten number system.
So we find that 0.27 is the same as (0.27 x 100)% = 27%.

Similarly, 0.735 is the same as (0.735 x 100)% = 73.5%
and 7.46 is the same as (7.46 x 100)% = 746%.

Changing a % to a decimal

(Again, dead easy!)

Here are 3 examples to show you how to deal with all possible snags.
Example (1) What is 37% as a decimal?

Example (2) What is 25.5% as a decimal?

Example (3) What is 50% as a decimal?

The easiest way to explain how to work these out is to look at some examples.

Example (1) Suppose the profits of a certain company go from £365 000 in January to £425 000 in February. What is the % increase in their profits? RULE:- Percentage increases and decreases are always calculated with respect to the value before the change took place. Here, the actual increase in profits is £425 000 - £365 000 = £60 000. The % profit is £60 000 as a percentage of £365 000 Example (2) The number of first year students at a certain university studying Law was 127 in 1996 and 114 in 1997. What was the % decrease? The actual decrease is 127 - 114 = 13. The % decrease is 13 as a % of 127. 13 as a fraction of 127 is 13/127. Now, just multiply by 100 so you get Example (3) The price of a certain model of car goes up by 8%. It used to cost £7 800. What will it cost in future?

There are two ways of finding this.

Method (1)
First find the actual increase in cost. This is 8% of £7 800 so it is

Method (2)
This is the all-in-one way of doing it.
The new price is 108% of the old one, so it is

Example (4) At the beginning of December, the price of a certain item is increased by 5% to make a bigger Christmas profit. At the beginning of January, there is a Sale and the unsold items are labelled 5% OFF! Would you now be paying the same as if you had bought the item in November? If not, would you be paying more or less? Have a go at answering this before looking.   Suppose it cost £100 in November. Then in December the price increased by 5% to £105. The Sale Price is now calculated as a reduction of 5% on this current price of £105. So, using method (1), the actual reduction in price is Therefore you would only pay £105 - £5.25 = £99.75. You would get it cheaper in January than you would have done if you had bought it in November.

Now it would be wise to practise all these rules by working out the answers to some problems yourself.

source: http://www.netcomuk.co.uk/~jenolive/percent1.html