Solve Your Query for Rational Number

Rational number

A rational number refers to the number which can be represented as quotient p/ q of that of two integers like that of q ≠ 0. It can be brought out that in addition to all fractions, set of the rational numbers is inclusive of integers and each of them can be written down as the quotient and integer acts as numerator and 1 acts as the denominator. The rational numbers in the decimal form can be terminating or they can be the repeating decimals.

The real number which cannot be expressed as quotient of the two integers is called the irrational number. The rational number is kind of the real numbers and it is found to be in form of the p/q in which q is not found to be equal to the 0. The fraction which has the non-zero denominators can be termed as a rational number. There exist various examples of the rational number and they are found to be ½, 1/5, ¾ and that of so on. The number “0” can also be termed as a rational number and it can be represented in various forms like 0/1, 0/2, 0/3 and so on. For the identification of whether a number is rational number or the not there are certain conditions which have to be checked. It can be represented in form of the p/q within which q ≠0.

Kinds of Rational Numbers

The rational number can be said to be in the standard form in the event of common factor in between numerator and the denominator to be only 1 and denominator has to be positive. The numerators can bear positive signs and these numbers can be called the rational numbers in the standard form.

Positive and Negative rational Numbers

Positive rational numbers are indicative of the numbers in which numerator and denominator are found to be positive integers or that of the negative integers. The rational numbers can be stated to be positive in the event of numerators and the denominators being of the same sign. There exist various examples of the positive rational numbers and they are found to be 3/8, 9/10, -34/ -40.

The rational numbers can be stated to be negative in the event of numerators and the denominators being negative. It can hence be stated that in the event of numerator or the denominator of the rational number being the negative integer, then it can be termed as the negative rational number. There exist various examples of the negative rational numbers and they are -3/8, 5/ (-7), (-2) /9, (-3)/ 7 and that of 1/ (-5).

Rational Numbers and Irrational Numbers

The rational numbers refers to kind of the real numbers which is in form of the p/q in which q is not found to be equal to the zero. The fraction having the non-zero denominators can be termed as the rational number. The rational numbers can be expressed as quotient or the fraction of the two integers which has the numerator p and the non-zero denominator. The decimal expansion of the rational number can be stated to be either terminate after finite number of the digits or it can help in repeating same finite sequence of the events. The irrational numbers cannot be expressed as quotient of the two integers. The rational number within arithmetic is a number which can be represented as quotient p/q of the two integers like that of q ≠ 0. The rational numbers can be made out by the division of one integer by that of another integer.

For example, it can be stated that there exists no number among the integers and the fractions which can be stated to be equal to square root of the 2. The counterpart problem in the measurement can be for finding length of diagonal of the square and its side can be of one unit long. There does not exist sub-division of unit length which would be able to divide evenly within length of diagonal. It can be stated to be necessary early within history of the mathematics for the extension of concept of the number for the inclusion of irrational numbers.

Examples of rational numbers

There exist various examples of the rational numbers and they are ½, 1/5 and ¾.

The numbers can be said to be rational which can be represented in form of the p/q and it has the arithmetic operations which can help to perform divisions, addition, subtraction and multiplication in between the different numbers. The rational numbers are operated in the manner in which the fractions are operated.  There exist various examples of the rational numbers and they can be stated to be ½, -3/4, 3/10 and that of 0.3. – 0.7 is also an example of the rational number and it is integral in regard to the field of mathematics education. The formula of the rational numbers can be stated to be:

Identification of rational numbers

The set of the rational numbers can be stated to be closed and associative. It can be stated that additive identity, O, and that of multiplicative identity, 1 can be stated to be present within set of the rational numbers. The rational numbers possess additive inverses within set of the rational numbers.

Practical Questions on Rational Numbers

Is 0 the rational number?

The 0 can be said to be the rational number. The rational expressions cannot be divided by the zero and denominator has to be of the non-zero integer. It can be stated to be because of the fact that quotient which is divided by the 0 can culminate in the non-integer. The number which is doing dividing can be stated to be zero and there exists below fraction p/q:

P / q= 0/4

p/ q= 0

The rational expression helps to prove that the 0 is the rational number as the number can be stated to be divided by the 0 and it can be said to be equal to the 0.

Is 3.14 a rational number?

3.14 can be written as fraction of the two integers and hence it can be labelled as the rational number.