9 MATHS CHAPTER 2

 

Kerala State Syllabus 9th Standard Maths Solutions Chapter 2 Decimal Forms

Kerala Syllabus 9th Standard Maths Decimal Forms Text Book Questions and Answers

Textbook Page No. 26

Decimal Forms Class 9 Kerala Syllabus Question 1.
Write the fractions below in decimal form:

1. 320
2. 340
3. 1340
4. 780
5. 516

Answer:
1. 320
= 3×520×5 = 15100 = 0.15

2. 40 = 2 x 2 x (2 x 5)
Multiplied by 5 x 5
(2 x 5) x (2 x 5) x (2 x 5) = 1000
it is a multiple of 10.
310 = 3x5x540x4x5x = 751000 = 0.75

3. 40 = 2 x 2 x (2 x 5)
Multiplied by 5 x 5
(2 x 5) x (2 x 5) x (2 x 5) = 1000
It is a multiple of 10.
1340 = 13x5x520 = 3251000 = 0.325

4. 80 = 2 x 2 x 2 x (2 x 5)
Multiplied by 5 x 5 x 5
It is a multiple of 10.
(2 x 5) x (2 x 5) x (2 x 5) x (2 x 5) = 1000
780 = 7x5x5x580x5x5x5 = 87510000 = 0.0875

5. 16 = 2 x 2 x 2 x 2
Multiplied by 5 x 5 x 5 x 5 x 5
(2 x 5) x (2 x 5) x (2 x 5) x (2 x 5) = 1000
It is a multiple of 10.
516 = 5x5x5x5x516x5x5x5x5 = 312510000 = 0.3125

Kerala Syllabus 9th Standard Maths Chapter 2 Question 2.
Find the decimal form of the sums below:

1. 180 + 125 + 1125
2. 15 + 152 + 153 + 154
3. 12 + 122 + 123

Answer:
1. 180 + 125 + 1125
Denominators of all the fractions should be 125
1×255×25 + 1×525×5 + 1×1125×1
= 25125 + 5125 + 1125 = 31125
125 = 5 x 5 x 5
Multiplied by 2 x 2 x 2
(5 x 2) x (5 x 2) x (5 x 2) = 1000
It is a power of 10
31125 = 31x2x2x2125x2x2x2 = 2481000 = 0.248

2. 15 + 152 + 153 + 154
Denominators of all the fractions should be 54

3. 12 + 122 + 123
Denominators of all the fractions should be 23

Hss Live Guru 9th Maths Kerala Syllabus Question 3.
A two – digit number divided by an other two-digit number gives 5.875. What are the numbers?
Answer:
5875 = 58751000
5875 = 5 x 5 x 5 x 47
1000 = 5 x 5 x 5 x 8

5.875 = 58751000 = 5x5x5x475x5x5x8 = 478
But 8 is not a two digit number. So we multiplied both numerator and denominator by 2, we get
478 = 9416
5.875 = 9416

Textbook Page No. 30

Kerala Syllabus 9th Standard Maths Notes Question 1.
For each of the fractions below, find fractions with denominators powers of 10 gefting chaser and closer to it and hence write its decimal form:

1. 23
2. 56
3. 19

Answer:
1. 23 = 2×103×10 = 210 x 103 = 210 x (3 + 13)

The fraction 610, 66100, 6661000, ……… and so on get closer and closer to 23.
i.e., 0.6, 0.66, 0.666, …………..
12 = 0.666

2. 56 = 5×106×10 = 510 x 106 = 510 x (1 + 46

The fractions 80100, 8301000, 83305, ………. and so on get closer and closer to 56.
∴ 56 = 0.8333………

3. 19 = 1×109×10 = 110 x 109

The fractions 110, 11100, 1111000, ………… and so on get closer and closer to 19.
∴ 19 = 0.1111 ……

Hsslive Maths Class 9 Kerala Syllabus Question 2.

1. Using algebra, explain why 110, 11100, 11000, ………… of any number get closer and closer to 19 of that number.
2. Use the general principle got above to single-digit numbers to find the decimal forms of 29, 49, 59, 79, 89.
3. What can we say in general about decimal forms with a single digit repeating?

Answer:
1. Let x be the number

The numbers x10, 11x100, 111x1000, ……… comes closer and closer to x9.
So the fraction 110, 11100, 1111000, ……. comes closer and closer to 19.

2. a.
110 part of a number comes closer to its 19

b. 110 part of a number comes closer to its 19

c. 110 part of a number comes closer to its 19

d. Since 19 is closes to 110

e. Since 19 is closes to 110

3. The denominator of a fraction is 9 or multiple of 9 then its decimal froms is always a single digit repetition of their own numerator.

Hsslive Guru 9th Maths Kerala Syllabus Question 3.

1. Find the decimal form of 111.
2. Find the decimal forms of 211, 311
3. What is the decimal form of 1011?

Answer:
1. 111 = 1×1011×10 = 110 x 1011

Continuing like this,
= 0.090909

2. a. 211 = 2×1011×10 + 210 x 1011

Continuing like this,
211 = 0.18181818 …….

b. 311 = 3×1011×10 = 310 x 1011

Continuing like this
311 = 0.272727…..

3. 1011 = 10×1011×10 = 1010 x 1011

Continuing like this
1011 = 0.90909……….

Hss Live Guru 9 Maths Kerala Syllabus Question 4.
Write the results of the operations below as decimals:

1. 0.111…. + 0.222 …….
2. 0.333…. + 0.777 …..
3. 0.333…. x 0.666…
4. (0.333….)2
5. 0.444……−−−−−−−−−√

Answer:
1. 0.111 = 19
0.222…. = 29
0.111 …. + 0.2222 …….. = 19 + 29 = 39
= 0.3333

2. 0.3333 = 39
0.7777…. = 79
0.3333 ……. + 0.7777…. = 19 = 29 = 39
= 1.1111……….

3. 0.3333 = 39
0.6666…. = 69
0.3333….. x 0.6666…… = 39 x 69
= 1881 = 29 = 0.2222……..

4. 0.3333 …….. = 39
(0.3333)2 ….. = (39)2
= 3×39×9 = 19 = 0.1111…………

5. 0.4444 ….. = 49

Kerala Syllabus 9th Standard Maths Decimal Forms Exam Oriented Question and Answers

Question 1.
Write the deciamal form of 16
Answer:
16 = 0.1666…….

Question 2.
Write in deciamals

1. 19
2. 29
3. 17
4. 111
5. 211
6. 112

Answer:

1. 0.111……
2. 0.222………
3. 0.14285…..
4. 0.090909…..
5. 0.181818….
6. 0.08333……

Question 3.
Find the fraction of denominator is a power of 10 equal to each of the fractions below, and then write their decimal forms:
i. 150
ii. 340
iii.516
iv. 12625
Answer:

Question 4.
Find the fraction of denominator is a power of 10 getting closer and closer to each of the fractions be low, and then write their decimal forms.

1. 56
2. 311
3. 2311
4. 113

Answer:
1. 56 = 510 x 106 = 110(506)

2. 311 = 3100 x 10011 = 3100(9 + 111)

3. 2311 = 23100 x 10011

4. 113 = 1100 x 10013

Question 5.

1. Explain using algebra, that the fractions 110, 11100, 1111000… gets closer and closer to 19
2. Using the general principle above on single digit numbers, find the decimal forms of 29, 49, 59, 79, 89 (Why 39 and 69 left out in this?)
3. What can we say in general about those decimal forms In which a single digit repeats?

Answer:
1. Let x be the number

2. 29 – 210 = 290

(39, 69 These fractions having common factor in the numerator and the denominator)

3. Repeated deciamals.

Question 6.

1. Find the decimal form of 14.
2. Write the decimal form of 710 + 3100 + 41000.

Answer:
1. 14 = 0.25

2. 710 = 0.7
3100 = 0.03
41000 = 0.004
710 + 3100 + 41000
= 0.7 + 0.03 + 0.004
= 0.734

Question 7.

1. Write the decimal forms of 13 and 19.
2. What is the decimal form of (0.3333…..)2?

Answer:
1. 13 = 0.3333…..
19 = 0.1111……

2. (0.3333…..)2 = (13)2 = 19 = 0.1111….

Question 8.
Write the decimal forms of 325 and 18.
Answer:

Question 9.
a. Write the decimal form of the fractions and 12 and 25.
b. 1f f is a fraction between and 25 What is k?
c. Write the decimal form of the fraction 4k.
Answer:

If 4k is between 12 and 25, then 4k is between 48 and 410. Then the number is 49.
∴ k = 9

c. 49 = 0.4444…….