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
01. 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.
02. Test Yourself
Expression of Decimal numbers in the form of p/q
(a) Express the Terminating decimals numbers in the form of p/q
(i) Expressed the given numbers in form of p/q.
(i) 0.5 (ii) 3.3 (iii) 0.5
(iv) 0.25 (v) 0.15 (vi) 0.35
(vii) 0.125 (viii) 0.150 (ix) 0.035
(x) 0.2150 (xi) 0.31426 (xii) 0.00025
(b) Express the Non-Terminating decimals numbers in the form of p/q
(ii) Expressed the given numbers in form of p/q.
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(i) Show that 0.333... = 0.3 can be expressed in the form where p and q are integers and q ≠ 0.
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(ii) Show that 0.666... = 0.6 can be expressed in the form where p and q are integers and q ≠ 0.
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(iii) Show that 3.777... = 3.7 can be expressed in the form where p and q are integers and q ≠ 0.
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(iv) Show that 1.272727... = 1.27 can be expressed in the form where p and q are integers and q ≠ 0.
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(v) Show that 18.484848... = 18.48 can be expressed in the form where p and q are integers and q ≠ 0.
____
(vi) Show that 621.621621621... = 621.621 can be expressed in the form, where p and q are integers and q ≠ 0.
____
(vii) Show that 0.235235235... = 0.235 can be expressed in the form, where p and q are integers and q ≠ 0.
(iii) Expressed the given numbers in form of p/q.
_ _ _
(i) 0.5 (ii) 3.3 (iii) 0.5
_ _ _
(iv) 0.2 5 (v) 0.3 2 (vi) 0.2 4 3
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
03. Test Yourself
Q.1 Find one rational numbers between 1 and 2.
Q.2 Find two rational numbers between 3 and 4.
Q.3 Find three rational numbers between 7 and 9.
Q.4 Find one rational numbers between 1/2 and 3/2.
Q.5 Find two rational numbers between 3/5 and 4/5.
Q.6 Find three rational numbers between 1/3 and 2/3.
Q.7 Find one rational numbers between 1/2 and 1/3.
Q.8 Find two rational numbers between 3/4 and 4/3.
Q.9 Find three rational numbers between 5/7 and 9/11.
04. Test Yourself
Q.1 Find four rational numbers between 1 and 2.
Q.2 Find five rational numbers between 3 and 4.
Q.3 Find six rational numbers between 7 and 9.
Q.4 Find four rational numbers between 1/2 and 3/2.
Q.5 Find five rational numbers between 3/5 and 4/5.
Q.6 Find six rational numbers between 1/3 and 2/3.
Q.7 Find six rational numbers between 1/2 and 1/3.
Q.8 Find four rational numbers between 3/4 and 4/3.
Q.9 Find five rational numbers between 5/7 and 9/11.
Pythagoras Triplets Aur Bodhan Per Thagorean Triplets
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