Rational and Irrational Number
The union of the set of rational numbers and the set of irrational numbers is called the real numbers.The Number in the form \(\frac{p}{q}\), where p and q are integers and q≠0 are called rational numbers.Numbers which can be expressed in decimal form are expressible neither in terminating nor in repeating decimals, are known as irrational numbers.
Summary
The union of the set of rational numbers and the set of irrational numbers is called the real numbers.The Number in the form \(\frac{p}{q}\), where p and q are integers and q≠0 are called rational numbers.Numbers which can be expressed in decimal form are expressible neither in terminating nor in repeating decimals, are known as irrational numbers.
Things to Remember
- The number in the form \(\frac{p}{q}\), where p and q are integers and q≠0 are called rational number.
- A rational number is a number that can be written as a ratio.
- An irrational number is a real number that cannot be expressed as a ratio of integers.
- Irrational numbers cannot be represented as terminating or repeating decimals.
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Rational and Irrational Number
Rational Numbers
The number can be in different form. Some numbers can be in a form of fraction, ratio, root and with the decimal. If the number is in the form of \(\frac{p}{q}\) (fraction) ,of two integer p and q where numerator p and q≠0 are called rational numbers.
5 \(\frac{2}{3}\), \(\frac{7}{4}\), \(\frac{3}{4}\), \(\frac{3}{5}\) etc are the examples of rational numbers.
Rational number can be:
- All natural number
- All whole number
- All integer
- All fraction
Irrational Numbers
Numbers which cannot be expressed in a ratio (as a fraction of integer) or it can be expressed in decimal form is known as irrational numbers. It can neither be terminated nor repeated.
For example,
√7 = 2.64575131.............
√5 = 2.23620679....... etc are irrational numbers.
√2,√3,√5,√6,√7, etc. are the examples of irrational number where the numbers are a non-terminating and a non-repeating number.
Some Results on Irrational Numbers
- If we made an irrational number negative then it is always an irrational number.
For example, -√5 - If we add a rational number and an irrational number then a result is always an irrational number.
For example, 2 +√3 is irrational. - If we multiply a non-zero rational number with an irrational number then it is always an irrational number.
For example, 5√3 is an irrational number. - The sum of two irrational number is not always an irrational number.
For example, (2 +√3) + (2 -√3) = 4, which is irrational. - The product of two irrational number is not always an irrational number.
For example, ( 2 +√3) x (2 -√3) = 4 -3 =1, which is rational.
Lesson
Real Number System
Subject
Compulsory Maths
Grade
Grade 8
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