CBSE Class 9 Maths solutions Number Systems Ex1.3 | NCERT Class 9 maths solutions

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00:02 Q1. Write the rational numbers in decimal form and say what kind of decimal expansion each has :

00:28 (i)Find the decimal expansion of 36/100

00:49 kind of decimal expansion : terminating

01:03 (ii)Obtain the decimal expansion of 1/11

01:15 process of long division

02:33 kind of decimal expansion : non-terminating and recurring (repeating)

(iii)Find the decimal expansion of 4 and 1/8

02:52 (iv)Obtain the decimal expansion 3/13

03:10 long division method

06:30 kind of decimal expansion : non-terminating and repeating

06:44 (v)Find the decimal expansions of 2/11

08:05 decimal expansion of rational number 2/11 : non-terminating and repeating

08:22 (vi)Obtain the decimal expansion 329/400

09:48 decimal expansion of rational number 329/400 is terminating

09:58 Q2. You know that 1/7 = 0.142857142857... Can you predict what the decimal expansions of 2/7, 3/7,4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?

Given decimal expansion of rational number 1/7 = 0.142857142857...

11:00 decimal expansion of rational number 2/7

11:42 decimal expansion of rational number 3/7

12:20 decimal expansion 4/7

12:58 decimal expansion of rational number 5/7

13:40 decimal expansion 6/7

A terminating or a non - terminating and repeating decimal expansion can be converted into the form p/q, where p and q are integers , and q is not 0 .

14:36 Q3. Express the following in the form p/q, where p and q are integers and q is not 0.

14:52 (i) Express decimal form of a number 0.6666.. in rational form p/q.

15:13 Multiplying both sides of equation by 10.

Here, one digit 6 is repeating

16:35 rational form p/q of decimal form 0.6666....

16:49 (ii) Convert decimal form of a number 0.477777 in rational form p/q .

19:08 rational number of decimal expansion 0.477777 is 43/90.

19:30 (iii) Write decimal form of a number 0.001001001001.... in rational form p/q

20:00 Multiplying both sides of equation by 1000.

Here, three digits 001 is repeating.

A number whose decimal expansion is terminating or non-terminating recurring is rational.

21:26 Q4. Express decimal expansion 0.99999 .... in the rational form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

22:23 Multiplying both sides of equation by 10.

Here, one digit 9 is repeating

22:45 Subtract one equation from other

23:38 rational form p/q of decimal expansion 0.99999 .... is 1.

Q5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

23:40 Q6. Look at several examples of rational numbers in the form p/q ( q ? 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

24:45 Condition for rational number p/q, q is not zero to have terminating decimal expansion.

25:08 Q7. Write three numbers whose decimal expansions are non-terminating non-recurring.

25:31 25:52 26:04 Examples of Ir-rational number

26:30 Q8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

27:14 Decimal expansion of rational number 5/7 by long division

29:12 Decimal expansion of 9/11.

30:50 Irrational numbers between two rational numbers.

A number having a non-terminating and non -repeating (non - recurring) decimal expansion is Ir-rational number.

31:36 Q9. Classify the following numbers as rational or irrational :

use the decimal expansions to distinguish between rationals and irrationals

31:53 (i) Find sqrt(23) is rational or irrational

decimal expansion of sqrt(23) is a non-terminating and non-repeating.

32:51 sqrt(23) is irrational.

33:12 (ii) Is sqrt(225) is rational or irrational ?

34:52 decimal expansion of sqrt(225) is terminating.

35:11 (iii) Say, whether 0.3796 is rational or irrational ?

Rational number, Irrational number defination.

36:01 (iv) 7.478478... is rational or irrational ?

37:18(v) Find 1.101001000100001... is rational or irrational

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cbse ncert solutions for class 9 maths Chapter 1 Number Syatems

Rational numbers | Irrational numbers | Rationalization | Real line | Real numbers

cbse maths for class 9 solutions Number Syatems

NCERT Solutions Class 9 Maths Chapter 1 Number Syatems

Common core Math Number Syatems

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