Percentage

This topic is pretty basic, but its applications are endless in real life. This very term (percentage) is used in countless comparisons, competitions, and evaluations. It is also used in experiments and applications of mathematical and physical laws in laboratories to measure accuracy or inaccuracy for drawing conclusions.

The word percentage comes from the Latin per centum, meaning “by the hundred”. A percentage is a way of expressing a number as a fraction of 100. It is denoted using the percent sign (%).

Hence, whenever the term ‘percentage’ comes into the picture, we are supposed to write a fraction with its denominator as 100.

$$\text {Basic operations in percentage}$$

$$\text {1. When the percentage of a number is to be calculated:}$$

$$\text {e.g. 35% of 100 is equal to:}$$

$$ \frac{35}{100} \times 100 = 35 $$

$$\text {2. When the given fraction has to be converted into percentage:}$$

$$\text {e.g. The percentage equivalent of $\frac{a}{b}$ is:}$$

$$ \frac{a}{b} \times 100 $$

$$ \text {Let $\frac{a}{b}$=c} $$

$$ \text {Therefore, the final value will be: $c \times 100 = d$} $$

Let us plug in some numbers in order to get more clarity about this generic formula.

$$\text {e.g. The percentage equivalent of $\frac{2}{5}$ is:}$$

$$ =\frac{2}{5} \times 100 $$

$$ \frac{2}{5} = 0.4 $$

$$ \text {Therefore, the final value will be: $0.4 \times 100 = 40$%$ $} $$

$$\text {Compounding percentages:} $$
When we are told to calculate $$\text {30% of 40% of 1200}$$ we simply need to use the definition of percentage to obtain the value of the expression.

$$ \frac{30}{100} \times \frac{40}{100} \times 1200 $$

$$ = \frac{1200}{10000} \times 1200 $$

$$ \text {Therefore, 30% of 40% of 1200 = $12 \times 12 = 144$} $$

$$\text {Note: When the value of a fraction is greater than one,}$$ $$\\ \text{the percentage is greater than 100.}$$

$$\text {This situation is usually seen in the stock market profits.}$$

$$ \text {e.g. If a person had invested \$10000, and their profits are \$20000,}$$ $$\\ \text{then their profit percentage is %200.} $$

Usually, percentage is often shown as a big object being cut into small, equal pieces, and those pieces are a representation of a certain amount. In many European and American countries, cents are used as 1/100 th part of a currency.
Percentage has applications in setting the rules for construction of a mechanical or an electrical part or an architectural construction. It is used for defining tolerances (allowed percentage variations in physical dimensions of an object like length, area, and volume).

One might come across the symbol ‰; this is known as per mille (mille referring to 1/1000).

In conclusion, the power of percentages lies in their remarkable ability to simplify, allowing us to compare, analyze, and understand the world with greater clarity. From calculating a discount and interpreting a poll to tracking economic growth and measuring scientific results, percentages are the workhorses of our quantitative lives.

A percentage alone is just a type of mathematical operation on a number; its true meaning is understood only with context.

So, the next time you encounter a percentage, pause. Appreciate its elegant utility as a tool for insight, but also question its foundation. Used thoughtfully, percentages don’t just count things; they help us see what truly counts. They are less a final answer and more a precise starting point for deeper understanding, proving that sometimes, the most profound insights are found not in the whole, but in the parts of a hundred.