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CBSE Notes for Class 10 Mathematics english Medium 1. Real Numbers

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1. Real Numbers

Numbers

There are two types of Numbers.

1. Real Numbers

2. Complex Numbers (Real numbers + Imaginary Numbers)

Real Numbers: The numbers which can be represented on the number line by a unique point are called real numbers.

Examples: -1, -2, -3, -4 ....................... , and 1, 2, 3, 4, 5.........................

Complex Numbers: Coplex numbers are the numbers which consist of both real and Imaginary numbers.

Examples: 2 + i√3, where 2 is real part and i√3 is imaginary part.

Real Numbers

(A)  Rational Numbers: The numbers which can be express in the form of p/q, and q0 such a numbers are known as real numbers.

(B)  Irrational Numbers: The numbers which are not rational numbers but these an be represented on a number line, such numbers are known as irrational numbers.

Rational Numbers

(I)  Integers:

(a) Whole numbers: These are the set of positive integers from 0. Which                  have not decimal and fractional part. Such numbers are known as                        whole numbers.

Example: 0, 1, 2, 3, 4, 5, ...........................

(i)  Natural Numbers: Natural numbers counting begin from 1 to ∞                             (infinty). such numbers are called natural numbers.

Ex: 1, 2, 3, 4, 5 ....................................... ∞.

(ii) Zero: 0

(b) Negative integers: The numbers before 0 on number line is called as                 negative integers these are -1, -2, -3, -4 ............................. -∞.

(II) Fractional Numbers:

(a) Proper fraction

(b) Improper fraction

Natural numbers

(a) Odd Numbers: The numbers which can not be divided by 2 are called odd           numbers.

Example: 1, 3, 5, 7, 9, 11, 13, 15 ................................................. ∞.

(b) Even Numbers: The numbers which can be divided by 2 are called even             numbers.

Example: 2, 4, 6, 8, 10, 12, 14, 16 ................................................ ∞.

(c) Prime Numbers:

(d) Composite Numbers:

(e) Co-prime Numbers:

(f)  Perfect Numbers:

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CBSE Notes⇒Class 10th ⇒ Mathematics ⇒ Chapter 1. Real Numbers:

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