# 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\times100 = 65%
2. Convert 4.05 into percentage4.05\times100 = 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\times5) % = 15%
2. Convert \frac {8}{25} into percentage\ ( \frac {8}{25}\ )\times 100 = (8\times4) % = 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\times12.5) % = 37.5 %
\frac {4}{8} = (4\times12.5) % = 50 %
\frac {5}{8}= (5\times12.5) % = 62.5 %
\frac {6}{8} = (6\times12.5) % = 75 %
\frac {7}{8} = (7\times12.5) % = 87.5 %
\frac {8}{8} = (8\times12.5) % = 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\times8 = 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%

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%

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