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 \displaystyle  x percentage by \displaystyle  x% , thus

\displaystyle  x\% = \frac{x}{100}

Convert a Percentage into a Fraction

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

\displaystyle  \text{Thus } x\%= \frac{x}{100}

\displaystyle \text{Example: }  5\% = \frac{5}{100}=0.05

Convert Fraction into Percentage

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

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

\displaystyle  \text{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 \displaystyle  100

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

\displaystyle  \text{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 \displaystyle  100 and put \displaystyle  % sign.

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

\displaystyle  \text{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.

\displaystyle  \text{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 \displaystyle  100 and add \displaystyle  \% sign.

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