Percentages are numbers that we frequently come across in everyday life. Percentages are used to give a common standard. The use of percentages is very common in many aspects of commercial life as well as in engineering. Interest rates, sale reductions, pay rises, exams and VAT are all examples of situation in which percentages are used. The word percent is derived from the Latin word 'Per centum' which means "out of one hundred". Symbolically percent is indicated as %.

If a student scores 75 marks out of a maximum of 100 in an examination, we say that he/she has scored 75% marks.

Percentage can be expressed as a fraction and a decimal also. From the above example we know that 75% is equivalent to $\frac{75}{100}$ .

Hence, 75% = $\frac{75}{100}$
= 0.75
In order to show some applications of percentage, various daily-life problems, particularly problems based on profit and loss and simple interest will be solved.

For example,
1. 70 percent means 70 out of hundred or $\frac{70}{100}$
2. 50% means 50 out of hundred means $\frac{50}{100}$

A percent can be defined as a ratio whose second term is 100.

“Percent is a fraction whose denominator is 100 and numerator indicates the required percent”

Therefore a Percent means parts of 100. The symbol used to denote percent is "%"

Example on Percentage


Let us see what fraction of the grid is shaded.
Percentage Example

Each grid is divided into 100 boxes. For each grid, the ratio of the number shaded boxes to the total number of boxes can be represented as fractions.

Ratio and Fraction

The fractions can represented as percents by multiplying each fraction with 100.

$\frac{(87)}{(100)}$ × 100 = 87%.

$\frac{(18)}{(100)}$ × 100 = 18%

$\frac{(40)}{(100)}$ × 100 = 40%

Ratios Fractions and Percentage