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.

`\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 %

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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 percentage**0.65`\times`100 = 65%**2. Convert 4.05 into percentage**4.05`\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

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 %

`\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 %

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

**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, 8/8**2/8 = (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}`

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**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 %

i.e. 10 % of 600 = 60

60`\times`8 = 480

Hence the percentage will be greater than 80% and less than 90 %

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**Step 2: **

Subtract the highest multiple (480) from numerator (512)

512 – 480 = 32

512 – 480 = 32

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**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 %

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i.e. 1 % of 600 = 6

6 `\times` 5 = 30

Hence the percentage will be greater than 85 % and less than 86 %

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**Step 4: **

Subtract the multiple (30) from resultant (32)

i.e. 32 – 30 = 2

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i.e. 32 – 30 = 2

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**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

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%

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**Step 1: **

10 % of 560 = 56

56 `\times` 11 = 616

Hence percentage is greater than 110% and less than 120%

56 `\times` 11 = 616

Hence percentage is greater than 110% and less than 120%

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**Step 2: **

640 – 616 = 24

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**Step 3: **

1 % of 560 = 5.6

5.6 `\times` 4 = 22.4

Hence percentage is greater than 114% and less than 115%

5.6 `\times` 4 = 22.4

Hence percentage is greater than 114% and less than 115%

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**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

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

Percentages Concepts and Formulae
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Thursday, December 28, 2017
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