90.1.1.IC DBSE New Maths Book Ch. 01

DBSE 

New Maths Book 

Ch. 01

NUMBER SYSTEM

Real Number system like 

1. Natural Numbers, 

2. Whole Numbers, 

3. Integers, 

4. Rational Numbers and 

5. Irrational Numbers

Finding A Number Between

There are infinitely many rational numbers between any two given rational numbers.

                                          1

R.N. Between A and B = – (A + B)

                                          2

Test Yourself 

Q.1 What are Natural numbers?

Q.2 What are Whole numbers?

Q.3 What are Integers?

Q.4 What is a Fraction?

Q.5 What are Rational numbers?

Q.6 Is every natural number a whole number?

Q.7 Is every whole number a natural number?

Q.8 Is every integer a whole number?

Q.9 Is every rational number a whole number?

Q.10 Is every whole number a rational number?

Try to convert the given rational numbers in decimal form:

Information:

The decimal representation of Rational numbers are of two types:

(i) Terminating decimals: Numbers with a finite number of digits after the decimal point are known as terminating decimals.

 Example: 2.56, 0.45, 2.735 etc. 

(ii) Non-Terminating recurring decimals:

(a) Non-Terminating recurring decimals: Number with infinite number of digits in which a digit or group of digits repeat after the decimal point without terminating. 

Example: 0.3333…, 0.454545… , 2.735473547354… etc.

(b) Non-Terminating non-recurring decimals: Number with infinite number of digits in which a digit or group of digits does not repeat after the decimal point without terminating. 

Example: π etc.

Rational Numbers Representation On a Number Line

Q. Write the rational number represented by each point labelled with a letter.

Expression of Decimal numbers in the form of p/q

(a) Express the Terminating decimals numbers in the form of p/q

Expressed the given numbers in form

(i) 3.5

(ii) 30.3

(iii) 0.45

(b) Express the Non-Terminating decimals numbers in the form of p/q

                                                   __

(i) Show that 1.272727... = 1.27 can be expressed in the form where p and q are integers and q ≠ 0.

                                                        __

(ii) Show that 0.2353535... = 0.235 can be expressed in the form, where p and q are integers and q ≠ 0.

Finding Rational numbers between any two integers or rational numbers:

To find a rational number between A and B

                                          1

R.N. Between A and B = – (A + B)

                                          2

Q. Find five rational numbers between 1/2 and 3/2.