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 $\displaystyle =(1-\frac{x}{100})a$