Question

What are the different types of rational numbers?

Answer 1

Hint: This type of question depends on the concept of Rational numbers. Rational numbers are the numbers which can be represented in the form \[\dfrac{p}{q}\] where \[q\ne 0\] . Rational numbers are similar to fractions so that we can say that any fraction that has a non-zero denominator is called a rational number. Also as 0 can be expressed as \[\dfrac{0}{1},\dfrac{0}{5},\dfrac{0}{10},......\] we can say that 0 is a rational number.

Complete step-by-step answer:
Now, here we have to write the different types of rational numbers. Rational numbers are the numbers which can be represented in the form \[\dfrac{p}{q}\] where \[q\ne 0\] . We have to note that when the rational number is divided the result must be in decimal form. The different types of rational numbers are as follows:
We know that every integer can be expressed in the form \[\dfrac{p}{q}\] where \[q\ne 0\] and hence every integer is a rational number.
For example, \[-2=\dfrac{-2}{1},-9=\dfrac{-72}{8},......\] etc.
Also we know that Natural numbers are nothing but positive integers so every natural number is also a rational number.
For example, \[15=\dfrac{45}{3},1000=\dfrac{5000}{5},....\]
Whole numbers are nothing but non-negative integers so we can say that every whole number is also a rational number.
For example, \[0=\dfrac{0}{150},78=\dfrac{234}{3},62=\dfrac{310}{5},.....\]

Standard Form of Rational Numbers –
We know that, a rational number is said to be in its standard form if the highest common factor between the divisor and dividend is equal to one only and hence the divisor must be positive.
For example, \[\dfrac{14}{12}\] is a rational number which can be simplified as \[\dfrac{7}{6}\] highest common factor between the divisor and dividend is 1.

Positive and Negative Rational Numbers –
As we know that the rational numbers are in the form \[\dfrac{p}{q}\] where p and q are integers & \[q\ne 0\] . The rational numbers can be positive or negative. If a rational number is positive then both p and q must have the same signs. If the rational number is negative then either p or q is a negative integer.
For example, \[\dfrac{19}{25},\dfrac{65}{23},\dfrac{103}{110}\] are positive rational numbers and \[\dfrac{-2}{9},\dfrac{5}{-11},\dfrac{-1}{1000}\] are negative rational numbers

Note: In this question students may make mistakes in real numbers and rational numbers. Students have to take care that every rational number is a real number but the reverse is not true. Real numbers are a union of rational numbers and irrational numbers.