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  Rational Numbers Definition Rational    numbers are one very common type of number that we usually study after integers in math. These numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. Types of Rational Numbers There are different types of rational numbers. We shouldn't assume that only fractions with integers are rational numbers. The different  types of rational numbers are: Integers like -2, 0, 3 etc. Fractions whose numerators and denominators are integers like 3/7, -6/5, etc.      T erminating decimals like 0.35, 0.7116, 0.9768, e Non-terminating decimals with some repeating patterns (after the decimal point) such as 0.333..., 0.141414..., etc. These are popularly known as non-terminating repeating decimals Smallest Rational Number Look at the chart given below to understand the difference between rational numbers and irrational numbers along with other types of numbers pictorially. Standard Form of Rational Numbers The standard form of a rational n

  Irrational Numbers Irrational numbers are those real numbers that cannot be represented in the form of a ratio.  In other words, those real numbers that are not rational numbers are known as irrational numbers Irrational Numbers Definition An irrational number is a real number that cannot be expressed as a ratio of integers. for example, √ 2 is an irrational number. Again, the decimal expansion of an irrational number is neither terminating nor recurring. In other words, we can say that irrational numbers cannot be represented as the ratio of two integers. Are Irrational Numbers Real Numbers? In Mathematics, all the irrational numbers are considered as real numbers, which should not be rational numbers.  It means that irrational numbers cannot be expressed as the ratio of two numbers.  The irrational numbers can be expressed in the form of non-terminating fractions and in different ways.  For example, the square roots which are not perfect squares will always result in an irrational