Percentages Concepts and Formulae

Percentage means out of 100. We can easily convert any fractional and decimal value into the percentage. The percentage is a very important topic for Bank PO, Bank Clerk, SSC, Railways etc.
The percentage is also a very important topic for Data interpretation, Simplification and for other Quants Arithmetic topics.

Convert Decimal value into Percentage:

To convert decimal value into percentile value simply multiple the decimal numbers by 100 and it will be converted into percentile value.
Examples:1. Convert 0.65 into percentage0.65`\times`100 = 65%
2. Convert 4.05 into percentage4.05`\times`100 = 405%

Convert fractional value into Percentage

To convert fractional value into percentile value multiply fractional by 100 and then convert it into lowest fractional form or decimal form.
Examples:1. Convert `\frac {3}{20}` into percentage`\ ( \frac {3}{20}\ )\times` 100 = ( 3`\times`5) % = 15%
2. Convert `\frac {8}{25}` into percentage`\ ( \frac {8}{25}\ )\times` 100 = (8`\times`4) % = 32 %

Basic conversion of fraction to percentage to remember:

`\frac { 1 }{ 1}` = 100 %

`\frac { 1 }{ 2}` = 50 %

`\frac { 1 }{ 3}` = 33.33 % = 33`\frac { 1 }{ 3} %`

`\frac { 1 }{ 4}` = 25 %

`\frac { 1 }{ 5}` = 20 %

`\frac { 1 }{ 6}` = 16.67 %

`\frac { 1 }{ 7}` = 14.28 %

`\frac { 1 }{ 8}` = 12.5 %

`\frac { 1 }{ 9}` = 11.11 % = 11`\frac { 1 }{ 9} %`

`\frac { 1 }{ 10}` = 10 %

`\frac { 1 }{ 11}` = 9.09 %

`\frac { 1 }{ 12}` = 8.33 %

`\frac { 1 }{ 13}` = 7.69 %

`\frac { 1 }{ 14}` = 7.14 %

`\frac { 1 }{ 15}` = 6.67 %

`\frac { 1 }{ 16}` = 6.25 %

`\frac { 1 }{ 17}` = 5.88 %

`\frac { 1 }{ 18}` = 5.55 %

`\frac { 1 }{ 19}` = 5.26 %

`\frac { 1 }{ 20}` = 5 %

If we remember the above easy conversions then we can convert some more fractions into percentage easily
Example:We remember than percentage of (1/16) is 6.25%
Then we can easily find conversions of 2/16, 3/16, 4/16, 5/16, ……… 16/16 as
`\ ( \frac {5}{16}\ )` = 5`\times\ ( \frac {1}{16}\ )` = 5 `\times` 6.25 = 31.25 %
`\ ( \frac {7}{16}\ )` = 7`\times \ ( \frac {1}{16}\ )` = 7 `\times` 6.25 = 43.75 %
`\ ( \frac {13}{16}\ )` = 13`\times\ ( \frac {1}{16}\ )` = 13 `\times` 6.25 = 81.25 %
`\ ( \frac {1}{8}\ )` = 12.5 %

So we can find easily percentage for 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/82/8 = (2`\times` 12.5) % = 25 %
`\frac {3}{8}` = (3`\times`12.5) % = 37.5 %
`\frac {4}{8}` = (4`\times`12.5) % = 50 %
`\frac {5}{8}`= (5`\times`12.5) % = 62.5 %
`\frac {6}{8}` = (6`\times`12.5) % = 75 %
`\frac {7}{8}` = (7`\times`12.5) % = 87.5 %
`\frac {8}{8}` = (8`\times`12.5) % = 100 %

Percentage of Some Difficult Fractions

If numerator < denominator, the percentage will always be less than 100%
If numerator > denominator, the percentage will always be greater than 100%

1. `\frac {512}{600}`

Step 1: 

Take 10% of the denominator and find the closest multiple to the numerator and less than numerator
i.e. 10 % of 600 = 60
60`\times`8 = 480
Hence the percentage will be greater than 80% and less than 90 %

Step 2: 

Subtract the highest multiple (480) from numerator (512)
512 – 480 = 32

Step 3: 

Take 1% of the denominator and find the closest multiple to the subtracted result of Step 2 (i.e. 32)
i.e. 1 % of 600 = 6
6 `\times` 5 = 30
Hence the percentage will be greater than 85 % and less than 86 %

Step 4: 

Subtract the multiple (30) from resultant (32)
i.e. 32 – 30 = 2

Step 5: 

Take 0.1% of the denominator and find the closest multiple to the resultant of Step 4
i.e. 0.1 % of 600 = 0.6
0.6 `\times` 3 = 1.8
Hence the percentage will be greater than 85.3 % and less than 85.4 %
Keep repeating the steps if further required

2.  `\frac {640}{560}`

Numerator > Denominator then percentage greater than 100%

Step 1: 

10 % of 560 = 56
56 `\times` 11 = 616
Hence percentage is greater than 110% and less than 120%

Step 2: 

640 – 616 = 24

Step 3: 

1 % of 560 = 5.6
5.6 `\times` 4 = 22.4
Hence percentage is greater than 114% and less than 115%

Step 4: 

24 – 22.4 = 1.6

Step 5: 

0.1% of 560 = 0.56
0.56 `\times` 2 = 1.12
Hence percentage is little bit greater than 114.2%
We can solve any fraction through this process

TRY OUT SOME EXAMPLES
1214/1560, 295/340 , 783/260 , 951/800