30. Percentage

Percentage is a fundamental concept in mathematics and is often used in a variety of contexts, from financial calculations to statistics. In the context of the National High School Examination (ENEM), understanding the percentage is crucial, as questions involving this topic are common.

For starters, the word 'percentage' comes from 'percent', which means 'per hundred'. So when we talk about 30%, for example, we are talking about 30 parts of a total of 100. In mathematical terms, 30% can be written as 0.30, since 30 divided by 100 equals 0.30.

One of the most common ways to use percentage is to describe change. For example, if the price of a product increases from R$100 to R$130, we can say that the price has increased by 30%. This is calculated by subtracting the original price from the new price (130-100 = 30), then dividing the result by the original price (30/100 = 0.30) and multiplying by 100 to get the percentage.

Another common application of the percentage is in discounts. If a product costs $100 and is 30% off, the discount would be $30 (30% of 100), and the new price would be $70 (100-30).

Percentages are also used to express proportions. If, in a classroom of 100 students, 30 are girls, we can say that the percentage of girls in the class is 30%. Likewise, the percentage of boys would be 70%.

In addition, percentages can be used to describe probabilities. If the chance of winning a game is 30%, that means that, on average, you would win 30 times if you played 100 times.

Another important application of the percentage is in financial mathematics. Interest, for example, is often expressed as a percentage. If you borrow $100 at an interest rate of 30% per annum, you will have to pay $30 in interest at the end of the year.

It is important to note that although percentages are often used to describe changes, they are not always equivalent to actual changes. For example, if a product increases in price by 30% and then decreases in price by 30%, the final price will not be the same as the original price. This is because the increase percentage is applied to the original price, while the decrease percentage is applied to the new higher price.

In short, percentage is a useful mathematical tool that helps us understand and describe the world around us. In the ENEM context, it's a topic you definitely need to master. Not just for math questions, but also for science and social science questions that might require some knowledge of statistics and probability.

With practice and understanding, percentages can become second nature, allowing you to make quick, informed calculations in a variety of situations. Remember, as with any topic in math, the key to success is practice. The more problems you solve, the better your understanding and the faster you can solve problems in the future.

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