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