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 Rational numbers are numbers that are written in the form of

 numerator and denominator, and the denominator is not equal to zero.

(irrational number) are numbers that do not contain integers in

 the numerator and denominator and that contain numbers that have square roots

For an incomplete square, we will know in this article what is

 the definition of a group of rational numbers and a group of irrational numbers, and we will know

On their characteristics, the difference between them, is zero a

 relative number or not, the intersection, the union, the

 difference between groups, important notes, and what is the number

Fractional, and we will learn about all of that and more in the Mathematics Genius Blog

? What is the definition of a set of rational numbers

As for the rational numbers or fractional numbers, they are

 numbers that can be written in the form of A / B so

 that A and B are two integers, and the number B is not equal

 to zero, so most numbers are used in daily life as

 relative numbers, as for non-relative numbers they are

 numbers It does not contain integers in the numerator or

 denominator, such as numbers that contain the square roots

 of an incomplete square such as the square root of

 the number 4, and the infinite decimal numbers such as the

 number ....... 0.141441555, and the number (Pi),

 and it should be noted that the numbers Relative and non-

relativistic. The properties of the real number system

 apply to them

The relative number or mixed number is called a positive rational

 number if the sign of the two numbers in the numerator and

 denominator are similar, but if the sign of the two numbers is

 different in the numerator and denominator, then the relative number

 in this case is called a negative rational number, and the relationship

 between the rational numbers and the rest of the numbers can be

 explained in science Mathematics as follows:

Rational numbers include all real numbers, real numbers include all integers, and integers include all 

natural numbers.

Fractions and mixed numbers                                    

   

All fractions that can be written in the form A / B, so that the value of A and B are integers, and the

 value of B is not equal to zero are rational numbers, and fractional numbers that can be written in the

 form A / B so that A and B are integers, and B Not equal to zero are also considered rational numbers,

 as shown in the following examples:

• The fraction 8/33 - is a relative number; This is because the numbers -33 and 8 are considered whole numbers, and the number 33 is not equal to zero.
• The mixed number 3 and 1/8 are considered to be a relative number; This is because it can be converted into a fraction 25/8 which is relative since the numbers 25 and 8 are both integers, and the number 8 does not equal zero.

Note: Some fractions and mixed numbers are not considered rational, as is explained in the following:

• The fraction 177/0 is not considered relative; Even though the numbers 177 and zero are both integers, the denominator is equal to zero, and this leads to an undefined value.
• The fraction pi / 2 is not considered relative. Although the denominator is an integer and not equal to zero, it is not a rational number.

Decimals 

  Decimals are relative if they are finite or periodic; This is because it can be written in A / B form, as

 shown in the following examples:  

• The decimal fraction 1.7 is considered a relative number, because it can be expressed in the form of 1.7 / 1, and when multiplying both the numerator and denominator by the number 10/10, the number 17/10 is produced, which is a rational number, as the numbers 17 and 10 are integers, and the number 10 is not equal to zero.
• The periodic decimal fraction ... 4.444 is considered a rational number; This is because it can be written in the form of the mixed number 4 and 1/4, and this mixed number can be converted to 10/4 which is a rational number.

  Characteristics of Rational Numbers and Irrational Numbers 

  The characteristics of rational numbers can be summarized as follows: 

• When multiplying the numerator and denominator of the relative number by an integer that is not equal to zero, this does not affect the relative number or change its value, for example when multiplying both the numerator and denominator of the relative number 3/5 by the number 3, the result is 9/15, which is a rational number, and when this is simplified In its simplest form, the result is 3/5.
• When dividing the numerator and denominator of the relative number by an integer that does not equal zero, the result does not affect the relative number or change its value, for example when dividing the numerator and denominator of the relative number 9/15 by the number 3, the result is 3/5, which is a rational number.
• When multiplying, adding, or subtracting two rational numbers, the result is always a rational number, so it is not possible to obtain a non-rational number.
• When you add two rational numbers with the same denominator, the result is the sum of the numerator in both numbers, and the denominator remains the same.
• Multiplying two rational numbers is the result of multiplying the numerator / product of the denominator.
• The square of a square root is always equal to a rational number, which is the number inside the root. 
• The product of non-relative roots results in obtaining a rational number sometimes, for example when multiplying the square root of number 2 by the square root of number 8, the result is the square root of number 16 and equals 2, which is a rational number. 
• If the common factor between the numerator and denominator of a rational number is only the number 1, then it is called the standard form of a rational number.

The difference between relative and irrational numbers

Relative and irrational numbers are both real numbers, but there is a difference between them

• The rational number: It is any positive or negative number that can be written as a fraction such as A / B so that the numerator and denominator are not equal to zero like the decimal fraction 1/2
• Irrational number: It is a number that cannot be written in the form of a fraction, such as the square root of the number 5, it is a decimal fraction that does not end at a specific number but continues infinitely and the square root of the number 7

Is zero a relative or non-relative number

Yes, the zero is from the rational numbers, from the whole numbers, and from the real numbers