Rational numbers - what are their properties?

Rational numbers are those that we can write as a fraction of two integers. In rational numbers, the divisor is not zero. What is the difference between rational and irrational numbers? What are the properties of rational numbers?

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1. What are rational numbers?

Rational numbers are numbers that can be written as a quotient of two integers, when the second number - the divisor, is other than zero.

We denote the set of rational numbers as Q and it is infinite. It includes all natural and integer numbers.

Examples of rational numbers would be 4, -20, 0.7 or 8. They can be written as a fraction, and so we get 4/1, -20/1, 7/10 or 8/1.

Real numbers. Definition and properties

Real numbers are all rational and irrational numbers. We can equate them with points on the axis ...

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2. Properties of rational numbers

What are the properties of rational numbers?

  • rational numbers with multiplication, addition, zero and one constitute a body;
  • in theoretical arithmetic, the body of rational numbers is defined as the body of fractions of the ring of integers;
  • the set of rational numbers is a countable set - it is equal to the set of natural numbers;
  • as a subset of the real number space R, rational numbers are dense in R.

Natural numbers. Definition and rules

What is the definition of a natural number? What are some examples of natural numbers? Is zero natural? ...

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3. What are irrational numbers?

Irrational numbers - The opposite of rational numbers are real numbers which, as the name suggests, are not rational numbers, so they cannot be represented as the quotient of an integer to an integer other than zero.

These numbers fill the gaps in the Dedekind sections of the set of irrational numbers Q, in effect giving the complete space.

The decimal expansion of these numbers is non-periodic and infinite. The international symbol for the set of irrational numbers is IQ.

The most famous example of an irrational number is Pi, which is approximately 3.14.

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