CBSE Class 9 Maths Chapter 1 Number Systems Revision Notes
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Real numbers are all numbers that can be represented on a number line and include all rational numbers like integers, fractions, decimals, and also all irrational numbers. The real numbers include all the rational numbers, such as the integer − 5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356…, the square root of 2, an irrational algebraic number).
Types of real numbers
- 0: whole number, an integer but not a natural number.
- Every natural number N has a successor N + 1.
- Every integer has a successor Z + 1 and predecessor Z – 1.
- Every integer is a rational number but vice-versa may not be true.
- 2/1 is an integer
- 3/2 = 1.5 and 1/3 are not integers
An irrational number is a real number that cannot be expressed as a ratio of integers, i.e. as a fraction. Therefore irrational numbers when written as decimal numbers, do not terminate nor do they repeat.
- Irrational numbers cannot be written in the form p/q, where p and q are integers and q ≠ 0
- There are infinitely many irrational numbers. For example √2, √3, √5 are all irrational.
- The ratio of the length of the circumference of a circle to the length of its diameter is always constant. It is an irrational number and denoted by π.
The basic arithmetic operations are the addition, subtraction, multiplication, and division for Real Numbers. The basic arithmetic properties are closure, commutative, associative, and distributive properties.
1. Commutative law of addition: a + b = b + a
2. Commutative law of multiplication: a × b = b × a
3. Associative law of addition: a + (b + c) = (a + b) + c
4. Associative law of multiplication: a × (b × c) = (a × b) × c
5. Distributive law of multiplication over addition :a × (b + c) = (a × b) + (a × c) or (a + b) × c = (a × c) + (b × c)
CBSE Class 9 Maths Chapter 1 Number Systems Revision Notes PDF