Hundredth Part: If you divide any thing into 100 equal parts, then each part would be known as hundredth part.

Percentage: By a certain percentage, we mean “that many hundredth”

We denote  x   percentage by x%  , thus  x\% = x \ hundred^{th} = \frac{x}{100}

 

Convert a Percentage into a Fraction

For converting a percentage into fraction, divide it by 100  and remove the \%  sign.

Thus  x\%= \frac{x}{100}

Example:  5\% = \frac{5}{100}=0.05

 

Convert Fraction into Percentage

For converting a fraction into a percentage, multiply the fraction by  100 and add  \% sign to the resultant.

\frac{a}{b} = \frac{a}{b}\times 100 \% 

Example:  0.05 = (0.05 \times 100) = 5\% 

 

Convert a Percentage into a Ratio

A percentage can be expressed as a ratio with the first term equal to the given percentage and the second term equal to 100 

Therefore, x\% = \frac{x}{100}

Example: 5\% = \frac{5}{100} = \frac{1}{20}

 

Convert Ratio into a Percentage

First write the ratio as a fraction and then multiply the fraction by  100  and put  % sign.

Therefore a \colon b=\frac{a}{b} \times 100 \% 

Example: 1\colon 4 = \frac{1}{4}\times 100 \% = 25\%

 

Convert a Percentage into a Decimal

First convert the percentage into fraction and then convert fraction into a decimal.

Example: 75\% = \frac{75}{100} = 0.75

 

Convert a Decimal into a Percentage

First convert the given decimal into a fraction and then multiply the fraction by 100 and add \% sign.

Example: 0.40 = \frac{40}{100} = \frac{40}{100} \times 100\% = 40\%

 

Increasing or Decreasing a certain Quantity by a Certain Percentage

  1. If you have to increase a number a by x\% , then the new number would be=(1+\frac{x}{100})a
  1. If you have to decrease a number a by  x\%  , then the new number would be =(1-\frac{x}{100})a

 

 

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