The word per-cent is an abbreviation of the Latin phrase ‘per Centum’ which means per hundred or hundredths.

Thus, the term per-cent means **per hundred or for every hundred**.

When we say that a man gives 30 per-cent of his income as income tax. This means that he pays Rs 30 out of every 100 rupees of his income as income tax.

The symbol **%** is used for the term per-cent.

## Per-cent as a Fraction:

We have, 35% = 35 hundredths = \(\frac{35}{100}\).

Thus, a fraction with its denominator 100 is equal to that per-cent as is the numerator,

So, \(\frac{8}{100}\)= 8%, \(\frac{12}{100}\)= 12%, \(\frac{135}{100}\)= 135%

To convert a fraction into a per-cent we **multiply the fraction by 100 and put the per-cent sign(%).**

Thus, \(\frac{4}{5} = (\frac{4}{5} X 100)\)% = 80%; \(\frac{9}{20} = (\frac{9}{20} X 100)\)% = 45%

To convert a per-cent into a fraction, **we divide it by 100 and remove the per-cent sign %.
**Therefore, 25% = \(\frac{25}{100}\), 13% = \(\frac{13}{100}\) etc.

## Per-cent as a Ratio:

A per-cent can be expressed as a ratio with its **second term 100 and first term equal to the given per-cent**.

For example, 7% = \(\frac{7}{100}\)= 7:100, 79% = \(\frac{79}{100}\)= 79:100

In order to convert a given ratio into a per-cent, we first **convert the given ratio into the fraction and then multiply the fraction obtained by 100**.

Thus, \(8:9 = \frac{8}{9} = (\frac{8}{9} X 100)\)% = 88.8% and, \(14:3 = \frac{14}{3} = (\frac{14}{3} X 100)\)% = 466.6%

To convert a given per-cent into a ratio, we first **convert the per-cent into a fraction and then express it as a ratio**.

For example, 64% = \(\frac{64}{100} = \frac{16}{25}\)= 16:25

## Per-cent in Decimal form:

To convert a given per-cent in decimal form, we express it as a **fraction with denominator as 100 and then the fraction is written in decimal form**

For example, 36% = \(\frac{36}{100}\)= 0.36, 9% = \(\frac{9}{100}\)= 0.09

In order to convert a given decimal into a per-cent, we **move the decimal point on the right side by two digits and put the per-cent sign %**.

For example, 0.122 = 12.2%, 0.275 = 27.5%, 0.037 = 3.7%.