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Number System Class 9 Notes For Maths Chapter 1

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9th Class Maths Formulas CBSE Notes
Chapter 1 Number System

number system

Natural numbers are - 1, 2, 3, …………….. denoted by N.

Whole numbers are - 0, 1, 2, 3, ……………… denoted by W.
• Integers - ……. -3, -2, -1, 0, 1, 2, 3, ……………… denoted by Z.

Rational numbers - All the numbers which can be written in the form p/q,q ≠0 are called rational numbers where p and q are integers.

Irrational numbers - A number s is called irrational, if it cannot be written in the form p/q where p and q are integers and q ≠0

• The decimal expansion of a rational number is either terminating or non terminating recurring. Thus we say that a number whose decimal expansion is either terminating or non terminating recurring is a rational number.

• The decimal expansion of a irrational number is non terminating non recurring.

• All the rational numbers and irrational numbers taken together.

• Make a collection of real number.

• A real no is either rational or irrational.

• If r is rational and s is irrational then r+s, r-s, r.s are always irrational numbers but r/s may be rational or irrational.

• Every irrational number can be represented on a number line using Pythagoras theorem.

• Rationalization means to remove square root from the denominator.
math formula

Section - A

Q.1      Is zero a rational number? Can you write in the form p/q, where p and q are integer and sign of notqual  ?

Q.2      Find five rational numbers between as p/q

Q.3      State whether the following statements are true or false give reasons for your answers.
(i) Every natural no. is whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
(iv) Every irrational number is a real number.
(v) Every real number is an irrational number.
(vi) Every point on the number line is of the form where is a natural no’s.

Q.4 Show how  rote number  can be represented on the number line?

Section - A

Q.5 Find the decimal expansion of p/q value  ? What kind of decimal expansion each has.
Q.6 Show that 1.272727 =desimal value can be expressed in the form p/q, where p and q are integers and

Q.7      Write  three  numbers  whose  decimal  expressions  are  non-terminating  &  non recurring?
Q.8      Find three different rational between 3/5 and 4/7.

Q.9      Classify the following numbers as rational or irrational.

Section - C

math equation

qudilaer equation
Q.13 Rationalize the denominator of p/q equation

Section - D

Q.1      Represent   point value of rote        on number line.

Q.2 Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is . This seems to contradict the fact that is irrational. How will you resolve this contradiction?

Q.3 Simplify
 value of squre

Self Evaluation

Q.1 Write the value of

Q.3 If a & b are rational number, find the value of a & b in each of the following equalities.
rational number

Q.4 Prove that is an irrational number using long division method?

9th Class Maths Formulas CBSE Notes

 

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