2. Rational and irrational numbers

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Rational and irrational numbers are two fundamental concepts in mathematics, which are often addressed in the Enem test. Understanding these concepts and knowing how they apply can be the key to solving many math questions on the test. Let's explore each of these concepts in detail.

Rational Numbers

Rational numbers are those that can be expressed as a fraction of two integers, where the denominator is not zero. This includes whole numbers as they can be expressed as a fraction with 1 as the denominator. For example, the number 2 can be expressed as 2/1, which is a fraction of two integers, so 2 is a rational number.

Rational numbers can be positive or negative and can be represented on a number line. They can also be expressed as decimals, but these decimals will be either terminating or repeating. A terminating decimal is one that has a finite number of digits after the decimal point, such as 0.75. A repeating decimal is one that has an infinitely repeating pattern of digits, such as 0.3333...

Irrational Numbers

Irrational numbers, on the other hand, are those that cannot be expressed as a fraction of two integers. They can also be represented on a number line, but cannot be expressed as terminating or repeating decimals. Instead, decimals of irrational numbers will continue indefinitely with no repeating pattern.

The most famous example of an irrational number is the number pi (π), which is the ratio of a circle's circumference to its diameter. Pi is approximately equal to 3.14159, but the digits after the decimal point continue indefinitely with no repeating pattern. Another common example is the number square root of 2, which is approximately equal to 1.41421, but again, the digits after the decimal point continue indefinitely with no repeating pattern.

How these concepts are applied in Enem

On the Enem test, you may find questions that require you to identify whether a number is rational or irrational, or that require you to use these concepts to solve problems. For example, you might be asked to determine whether a decimal number is rational or irrational based on whether it has a repeating pattern or not.

You may also encounter questions involving operations with rational and irrational numbers. For example, you might be asked to add, subtract, multiply, or divide rational numbers, or calculate the square root of a rational number. Likewise, you may be asked to perform operations with irrational numbers, such as multiplying or dividing two irrational numbers, or adding or subtracting an irrational number from a rational number.

In summary, understanding the concepts of rational and irrational numbers and knowing how they are applied is fundamental to success in the ENEM math test. With practice and study, you can become comfortable with these concepts and be well-prepared for any question the exam might throw your way.

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33. Complex numbers