Number System
IX Mathematics Chapter 1: Number Systems Chapter Notes
Key Concepts 1. 2. 3. 4. 5. Numbers 1, 2, 3……., which are used for counting are called Natural numbers and are denoted by N. 0 when included with the natural numbers form a new set of numbers called Whole number denoted by W -1,-2,-3……………..- are the negative of natural numbers. The negative of natural numbers, 0 and the natural number together constitutes integers denoted by Z. The numbers which can be represented in the form of p/q where q 0 and p and q are integers are called Rational numbers. Rational numbers are denoted by Q. If p and q are coprime then the rational number is in its simplest form. Irrational numbers are the numbers which are non-terminating and non-repeating. Rational and irrational numbers together constitute Real numbers and it is denoted by R. Equivalent rational numbers (or fractions) have same (equal) values when written in the simplest form. Terminating fractions are the fractions which leaves remainder 0 on division. Recurring fractions are the fractions which never leave a remainder 0 on division. There are infinitely many rational numbers between any two rational numbers. If Prime factors of the denominator are 2 or 5 or both only. Then the number is terminating else repeating/recurring.
6. 7.
8. 9. 10. 11. 12.
Get the Power of Visual Impact on your side Log on to www.topperlearning.com
2
13. 14. 15. 16. 17.
Two numbers p & q are said to be co-prime if, numbers p & q have no common factors other than 1. The decimal expansion of rational number is either terminating or non-terminating recurring The decimal expansion of an irrational number is non-terminating, non-recurring. Real numbers satisfy the commutative, associate and distributive law of addition and multiplication. Commutative law of addition: If a and b are two real numbers then, a+b=b+a Commutative law of multiplication: If a and b are two real numbers then, a. b = b. a
19.
20.
Associative
Key Concepts 1. 2. 3. 4. 5. Numbers 1, 2, 3……., which are used for counting are called Natural numbers and are denoted by N. 0 when included with the natural numbers form a new set of numbers called Whole number denoted by W -1,-2,-3……………..- are the negative of natural numbers. The negative of natural numbers, 0 and the natural number together constitutes integers denoted by Z. The numbers which can be represented in the form of p/q where q 0 and p and q are integers are called Rational numbers. Rational numbers are denoted by Q. If p and q are coprime then the rational number is in its simplest form. Irrational numbers are the numbers which are non-terminating and non-repeating. Rational and irrational numbers together constitute Real numbers and it is denoted by R. Equivalent rational numbers (or fractions) have same (equal) values when written in the simplest form. Terminating fractions are the fractions which leaves remainder 0 on division. Recurring fractions are the fractions which never leave a remainder 0 on division. There are infinitely many rational numbers between any two rational numbers. If Prime factors of the denominator are 2 or 5 or both only. Then the number is terminating else repeating/recurring.
6. 7.
8. 9. 10. 11. 12.
Get the Power of Visual Impact on your side Log on to www.topperlearning.com
2
13. 14. 15. 16. 17.
Two numbers p & q are said to be co-prime if, numbers p & q have no common factors other than 1. The decimal expansion of rational number is either terminating or non-terminating recurring The decimal expansion of an irrational number is non-terminating, non-recurring. Real numbers satisfy the commutative, associate and distributive law of addition and multiplication. Commutative law of addition: If a and b are two real numbers then, a+b=b+a Commutative law of multiplication: If a and b are two real numbers then, a. b = b. a
19.
20.
Associative