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