RS Aggarwal Solutions for Class 6 Maths Chapter 7–Decimals

Class 6: Maths Chapter 7 solutions. Complete Class 6 Maths Chapter 7 Notes.

RS Aggarwal Solutions for Class 6 Maths Chapter 7–Decimals

RS Aggarwal 6th Maths Chapter 7, Class 6 Maths Chapter 7 solutions

Ex 7A Solutions

Question 1.
Solution:
(i)Fifty eight point six three = 58.63
(ii)One hundred twenty four point four two five = 124.425
(iii)Seven point seven six = 7.76
(iv)Nineteen point eight = 19.8
(v)Four hundred four point zero four four = 404.044
(vi)Point one seven three = 173
(v)Point zero one five = .015 Ans.

Question 2.
Solution:
(i) 14.83
Place value of 1 = 10,
Place value of 4 = 4,

Question 3.
Solution:
(i) 67.83 = (6 x 10) + (7 x 1)

Question 4.
Solution:

Question 5.
Solution:
(i) 7.5, 64.23, 0.074 = 7.500, 64.230, 0.074
(Here, at the most 0.074 has 3 places)
(ii) 0.6, 5.937, 2.36, 4.2 = 0.600, 5.937, 2.360, 4.200
(Here, 5.937 has at most 3 places)
(iii) 1.6, 0.07, 3.58, 2.9 = 1.60, 0.07, 3.58, 2. 90
(Here, at the most are two places)
(iv) 2.5. 0.63, 14.08, 1.637 = 2.500, 0.630. 14.080, 1.637 Ans.
(Here, at the most are three places)

Question 6.
Solution:
Making like decimals where ever it is necessary,

Question 7.
Solution:
First of all making them in like decimals,
(i) 5.8, 7.2, 5.69, 7.14, 5.06
=> 5.80, 7.20, 5.69, 7.14, 5.06
Arranging in ascending order,
5:06 <5.69 <5.80 <7.14 <7.20
=> 5.06 < 5.69 < 5.8 < 7.14 < 7.2 Ans.
(ii) 0.6, 6.6, 6.06, 66.6, 0.06
=>0.60, 6.60, 6.06, 66.60, 0.06
Arranging in ascending order,
0.06 < 0.60 < 6.06 < 6.60 < 66.60
=> 0.06 < 0.6 < 6.06 < 6.6 < 66.6 Ans.
(iii) 6.54, 6.45, 6.4, 6.5, 6.05
=> 6.54, 6.45, 6.4, 6.5, 6.05
Arranging in ascending order,
6. 05 < 6.40 < 6.45 < 6.50 < 6.54
=> 6.05 < 6.4 < 6.45 < 6.5 < 6.54 Ans.
(iv) 3.3,3.303, 3.033, 0.33, 3.003
=> 3.300, 3.303, 3.033, 0.330, 3.003
Arranging in descending order,
0.330 < 3.003 < 3.033 < 3.300 < 3.303
=> 0.33 < 3.003 < 3.033 < 3.3 < 3.303 Ans.

Question 8.
Solution:
Making them in like decimals and them comparing
(i) 7.3, 8.73, 73.03, 7.33, 8.073
=> 7.300, 8.730, 73.030, 7.330, 8.073
Arranging in descending order
73.030 > 8.730 > 8.073 > 7.330 > 7.300
=> 73.03 > 8.73 > 8.073 > 7.33 > 7.3 Ans.
(ii) 3.3, 3.03, 30.3, 30.03, 3.003
=> 3.300, 3.030, 30.300, 30.030, 3.003
Arranging in descending order
30.300> 30.030 >3.300 >3.030 > 3.003
=> 30.3 > 30.03 > 3.3 > 3.03 > 3.003 Ans.
(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007
=> 2.700, 7.200, 2.270, 2.720, 2.020, 2.007
Arranging in descending order
7. 200 > 2.720 > 2.700 > 2.270 > 2.020 > 2.007
=> 7.2 > 2.72 > 2.7 > 2.27 > 2.02 > 2.007 Ans.
(iv) 8.88, 8.088, 88.8, 88.08, ,8.008
=> 8.880, 8.088, 88.800, 88.080, 8.008
Arranging in descending order,
88.800 > 88.080 > 8.880 > 8.088 > 8.008
=> 88.8 > 88.08 > 8.88 > 8.088 > 8.008

Ex 7B Solutions

Convert each of the following into a fraction in its simplest form :

Question 1.
Solution:
.9 = 910

Question 2.
Solution:
0.6
= 610
= 6÷210÷2
= 35
(Dividing by 2, the HCF of 6, 10)

Question 3.
Solution:
.08
= 8100
= 8÷4100÷4
= 225
(Dividing by 4, the HCF of 7, 100)

Question 4.
Solution:
0.15
= 15100
= 15÷5100÷5
= 320
(Dividing by 5, the HCF of 15, 100)

Question 5.
Solution:
0.48
= 48100
= 48÷4100÷4
= 1225
(Dividing by 4, the HCF of 48, 100)

Question 6.
Solution:
0.53
= 531000

Question 7.
Solution:
= 1251000
= 125÷1251000÷125
= 18
(Dividing by 125, the HCF of 125, 1000)

Question 8.
Solution:
.224
= 2241000
= 224÷81000÷8
= 28125
(Dividing by 8, the HCF of 224, 1000)

Convert each of the following as a mixed fraction

Question 9.
Solution:
6.4
= 6410
= 64÷210÷2
= 326
= 625
(Dividing by 2, the HCF of 64, 10)

Question 10.
Solution:
16.5
= 16510
= 165÷510÷5
= 332
= 1612
(Dividing by 5, the HCF of 165, 10)

Question 11.
Solution:
8.36
= 836100
= 836÷4100÷4
= 20925
= 8925
(Dividing by 4, the HCF of 836, 100)

Question 12.
Solution:
4.275
= 42751000
= 4275÷251000÷25
= 17140
= 41140
(Dividing by 25 )

Question 13.
Solution:
25.06
= 2506100
= 2506÷2100÷2
= 125350
= 25350
(Dividing by 2 )

Question 14.
Solution:
7.004
= 70041000
= 7004÷41000÷4
= 1751250
= 71250
(Dividing by 4)

Question 15.
Solution:
2.052
= 20521000
= 2052÷41000÷4
= 513250
= 213250
(Dividing by 4)

Question 16.
Solution:
3.108
= 31081000
= 3108÷41000÷4
= 777250
= 327250
(Dividing by 4)

Question 17.
Solution:
2310
= 2.3

Question 18.
Solution:
167100
= 1.67

Question 19.
Solution:
1589100
= 15.89

Question 20.
Solution:
54131000
= 5.413

Question 21.
Solution:
214151000
= 21.415

Question 22.
Solution:
254
= 6.25

Question 23.
Solution:
335
= 3×5+35
= 15+35
= 185
= 3.6

Question 24.
Solution:
1425
= 1×25+425
= 25+425
= 2925
= 1.16

Question 25.
Solution:
51750
= 5×50+1750
= 250+1750
= 26750
= 5.34

Question 26.
Solution:
1238
= 12×8+38
= 96+38
= 998
= 12.375

Question 27.
Solution:
21940
= 2×40+1940
= 80+1940
= 9940
= 2.475

Question 28.
Solution:
1920
= 0.95

Question 29.
Solution:
3750
= 0.74

Question 30.
Solution:
107250
= 0.428

Question 31.
Solution:
340
= 0.075

Question 32.
Solution:
78
= 0.875

Question 33.
Solution:
(i) 8 kg 640 g in kilograms
= 86401000 kg
= 8.640kg
(ii) 9 kg 37 g in kilograms
= 9371000 kg
= 9.037 kg.
(iii) 6 kg 8 g in kilograms
= 681000 kg
= 6.008 kg Ans.

Question 34.
Solution:
(i) 4 km 365 m in kilometres
= 43651000 km
= 4.365 km
(ii) 5 km 87 m in kilometres

Question 35.
Solution:
(i) 15 kg 850 g in kilograms
= 158501000 kg
= 15.850 kg

Question 36.
Solution:
(i) Rs. 18 and 25 paise in rupees
= 1825100
= 18.25 rupees

Ex 7C Solutions

Add the following decimals :

Question 1.
Solution:
9.6, 14.8, 37 and 5.9
Converting these decimals into like decimals and then adding 9.6 + 14.8 + 37.0 + 5.9
= 67.3 Ans.
Working :

Question 2.
Solution:
23.7, 106.94, 68.9 and 29.5
Converting them into like decimals and then adding
23.70 + 106.94 + 68.90 + 29.50
= 229.04 Ans.
Working :

Question 3.
Solution:
72.8, 7.68, 16.23 and 0.7
Converting them into like decimals and then adding
72.80 + 7.68 + 16.23 + 0.70
= 97.41 Ans.
Working :

Question 4.
Solution:
18.6, 84.75, 8.345 and 9.7
Converting them into like decimals and then adding
18.600 + 84.750 + 8.345 + 9.700
= 121.395 Ans.
Working :

Question 5.
Solution:
8.236, 16.064, 63.8 and 27.53
Converting them into like decimals and then adding
8.236 + 16.064 + 63.800 + 27.530
= 115.630 Ans.
Working :

Question 6.
Solution:
28.9, 19.64, 123.697 and 0.354
Converting them into like decimals and then adding
28.900 + 19.640 + 123.697 + 0.354
= 172.591 Ans.
Working :

Question 7.
Solution:
4.37, 9.638, 17.007 and 6.8
Converting them into like decimals and then adding
4. 370 + 9.638 + 17.007 + 6.800
= 37.815 Ans.
Working :

Question 8.
Solution:
14.5, 0.038, 118.573 and 6.84
Converting them into like decimals and then adding
14.500 + 0.038 + 118.573 + 6.840
= 139.951 Ans.
Working :

Question 9.
Solution:
Earning for the first day = 32.60 rupees
Earning for the second day = 56.80 rupees
Earning for the third day = 72 rupees
Total earning = Rs. 32.60 + Rs. 56.80 + Rs. 72
= Rs. 161.40 Ans.
Working

Question 10.
Solution:
Cost of almirah = Rs. 11025
Cartage = Rs. 172.50
Cost on repair = Rs. 64.80
Total cost = Rs. 11025 + Rs. 172.50 + Rs. 64.80
= Rs. 11262.30 Ans.
Working :

Question 11.
Solution:
Distance covered by taxi = 36 km 235 m
= 36.235 km
Distance covered by Rickshaw = 4 km 85 m
= 4.085 km
and distance covered on foot
= 1 km 80 m
= 1.080 m
Total distance covered = 36.235 km + 4.085 km + 1.080 km
= 41.400 km
= 41 km 400 m Ans.
Working :

Question 12.
Solution:
Weight of sugar in a bag = 45 kg 80 g
= 45.080 kg
Mass (weight) of empty bag = 950 g
= 0.950 kg
Total weight of the bag with sugar = 45 kg 80 g + 950 g
= 45.080 kg + 0.950 kg
= 46.030 kg
= 46 kg 30 g Ans.
Working :

Question 13.
Solution:
Length of cloth for shirt = 2 m 70 cm
= 2.70 m
Length of cloth for pyjamas = 2 m 60 cm
= 2.60 m
Total length of cloth = 2.70 m + 2.60 m
= 5.30 m
= 5 m 30 cm Ans.
Working :

Question 14.
Solution:
Cloth of salwar = 2 m 5 cm = 2.05 m
Cloth for shirt = 3 m 35 cm = 3.35 m
Total length of cloth = 2.05 m + 3.35 m
= 5.4.0 m
= 5 m 40 cm Ans.
Working :

Ex 7D Solutions

Question 1.
Solution:
27.86 from 53.74
= 53.74 – 27.86
= 25.88 Ans.

Question 2.
Solution:
64.98 from 103.87
103.87 – 64.98
= 38.89 Ans.

Question 3.
Solution:
59.63 from 92.4
92.40 – 59.63
= 32.77 Ans.

Question 4.
Solution:
56.8 from 204
204.0 – 56.8
= 147.2 Ans.

Question 5.
Solution:
127.38 from 216.2
216.20 – 127.38
= 88.82 Ans.

Question 6.
Solution:
39.875 from 70.68
70.680 – 39.875
= 30.805 Ans.

Question 7.
Solution:
523.120 – 348.237
= 174.883 Ans

Question 8.
Solution:
600.000 – 458.573
= 141.427 Ans.

Question 9.
Solution:
206.321 – 149.456
= 56.865 Ans.

Question 10.
Solution:
3.400 – 0.612
= 2.788 Ans

Question 11.
Solution:
Converting them in like decimals
37.600 + 72.850 – 58.678 – 6.090
= (37.600 + 72.850) – (58.678 + 6.090)
= 110.450 – 64.768
= 45.682

Question 12.
Solution:
75.3 – 104.645 + 178.96 – 47.9
= 75.300 – 104.645 + 178.960 – 47.900
(Converting into like decimals)
= 75.300 + 178.960 – 104.645 – 47.900
= (75.300 + 178.960) – (104.645 + 47.900)
= 254.260 – 152.545
= 101.715 Ans.

Question 13.
Solution:
213.4 – 56.84 – 11.87 – 16.087
= 213.400 – 56.840 – 11.870 – 16.087
(Converting into like decimals)
= 213.400 – (56.840 + 11.870 + 16.087)
= 213.400 – 84.797
= 128.603 Ans.

Question 14.
Solution: 76.3 . 7.666 . 6.77
= 76.300 – 7.666 – 6.770
(Converting into like decimals)
= 76.300 – 14.436
= 61.864 Ans.

Question 15.
Solution:
In order to get the required number, we have to subtract 74.5 from 91.
Required number = 91 – 74.5
= 91.0 – 74.5
= 16.5 Ans.

Question 16.
Solution:
In order to get the required numbers, we have to subtract 0.862 from 7.3.
Required number = 7.3 – 0.862
= 7.300 – 0.862
= 6.438 Ans.

Question 17.
Solution:
In order to get the required number, we have to subtract 23.754 from 50
Required number = 50 – 23.754
= 50.000 – 23.754
= 26.246 Ans.

Question 18.
Solution:
In order to get the required number, we should subtract 27.84 from 84.5
Required number = 84.5 – 27.84
= 84.50 – 27.84
= 56.66 Ans.

Question 19.
Solution:
Weight of Neelam’s bag = 6 kg 80 g
Weight of Garima bag = 5 kg 265 g
Difference in their weights = 6 kg 80 g – 5 kg 265 g
= 6.080 kg – 5.265 kg
= 0.815 kg
= 815 g
Neelam’s bag is heavier by 815 g Ans.

Question 20.
Solution:
Cost of a notebook = Rs. 19.75
Cost of a pencil = Rs. 3 .85
Cost of a pen = Rs. 8.35
Total cost = Rs. 19.75 + Rs. 3.85 + Rs. 8.35
= Rs. 31.95
Amount given to the bookshop = Rs. 50
Balance amount to get back = Rs. 50.00 – Rs. 31.95
= Rs. 18.05 Ans.

Question 21.
Solution:
Weight of fruits = 5 kg 75 g .
Weight of vegetables = 3 kg 465 kg
Total weight of both = 5 kg 75 g + 3 kg 465 g
= 5.075 kg + 3.465 kg
= 8.540 kg
Gross weight of bag with these things = 9 kg
Net weight of bag = 9.000 – 8.540
= 0.460 kg
= 460 g Ans.

Question 22.
Solution:
Total distance = 14 km
Distance covered by scooter = 10 km 65 m
Distance covered by bus = 3 km 75 m
Total distance covered by scooter and by bus = 10 km 65 m + 3 km 75 m
= 10.065 km + 3 075 m
= 13.140 km
Remaining distance covered by walking
= (14.000 – 13.140) km
= 0.860 km
= 860 m Ans.

Ex 7E Solutions

Question 1.
Solution:
(c) 710 = 0.7

Question 2.
Solution:
(d) 5100 = .05

Question 3.
Solution:
(b) 91000 = 0.009

Question 4.
Solution:
(a) 161000 = 0.016

Question 5.
Solution:
(c) 1341000 = 0.134

Question 6.
Solution:
(a) 217100 = 2.17

Question 7.
Solution:
(b) 431000 = 4.03

Question 8.
Solution:
(b) 6.25 = 625100 = 614

Question 9.
Solution:
(b) 625
= 6×425×4
= 24100
= 0.24

Question 10.
Solution:
(c) 478 = 398 = 4.875

Question 11.
Solution:
(a) 24.8 = 24810
= 2445

Question 12.
Solution:
(b) 2125
= 2 + 125 x 44
= 2 + 4100
= 2.04

Question 13.
Solution:
(c) 2 + 310 + 4100
= 2 + 30100 + 4100
= 2.34

Question 14.
Solution:
(b) 26100
= 2 + 0.06
= 2.06

Question 15.
Solution:
(c) 4100 + 710000
= 0.04 + 0.0007
= 0.0407

Question 16.
Solution:
(c) 2.06
= (2×1)+(6×1100)
= 2+6100

Question 17.
Solution:
(d) Among 2.600, 2.006, 2.660,2.080, 2.660 is the largest.

Question 18.
Solution:
(b) 2.002 < 2.020 < 2.200 < 2.222 is the correct.

Question 19.
Solution:
(a) 2.1 = 2.100 and 2.005
2.100 > 2.055
=> 2.1 > 2.055

Question 20.
Solution:
(b) 1cm = 1100 m
= 0.01

Question 21.
Solution:
(b) 2 m 5 cm = 2.05 m

Question 22.
Solution:
(c) 2 kg 8 g = 2 + 0.008 = 2.008

Question 23.
Solution:
(b) 2 kg 56 g = 2.056 kg
(∵ 1000 g = 1 kg)

Question 24.
Solution:
(c) 2 km 35 m = 2.035 km
(∵ 1000 m = 1 km)

Question 25.
Solution:
(c) ∵ 0.4 + 0.004 + 4.4
= 4.804

Question 26.
Solution:
(a) ∵ 3.5 + 4.05 – 6.005
= 3.500 + 4.050 – 6.005
= 7.550 – 6.005
= 1.545

Question 27.
Solution:
(b) ∵6.3 – 2.8 = 3.5

Question 28.
Solution:
(c) ∵ 5.01 – 3.6 = 5.01 – 3.60
= 1.41

Question 29.
Solution:
(a) ∵ 2 – 0.7 = 2.0 – 0.7 = 1.3

Question 30.
Solution:
(a) ∵ 1.1 – 0.3
= 0.8

RS Aggarwal Solutions for Class 6 Maths Chapter 1: Download PDF

RS Aggarwal Solutions for Class 6 Maths Chapter 1–Number System

Download PDF: RS Aggarwal Solutions for Class 6 Maths Chapter 1–Number System PDF

Chapterwise RS Aggarwal Solutions for Class 6 Maths :

• Chapter 1–Number System
• Chapter 2–Factors and Multiples
• Chapter 3–Whole Numbers
• Chapter 4–Integers
• Chapter 5–Fractions
• Chapter 6–Simplification
• Chapter 7–Decimals
• Chapter 8–Algebraic Expressions
• Chapter 9–Linear Equations in One Variable
• Chapter 10–Ratio, Proportion and Unitary Method
• Chapter 11–Line Segment, Ray and Line
• Chapter 12–Parallel Lines
• Chapter 13–Angles and Their Measurement
• Chapter 14–Constructions (Using Ruler and a Pairs of Compasses)
• Chapter 15–Polygons
• Chapter 16–Triangles
• Chapter 17–Quadrilaterals
• Chapter 18–Circles
• Chapter 19–Three-Dimensional Shapes
• Chapter 20–Two-Dimensional Reflection Symmetry (Linear Symmetry)
• Chapter 21–Concept of Perimeter and Area
• Chapter 22–Data Handling
• Chapter 23–Pictograph
• Chapter 24–Bar Graph

About RS Aggarwal Class 6 Book

Investing in an R.S. Aggarwal book will never be of waste since you can use the book to prepare for various competitive exams as well. RS Aggarwal is one of the most prominent books with an endless number of problems. R.S. Aggarwal’s book very neatly explains every derivation, formula, and question in a very consolidated manner. It has tonnes of examples, practice questions, and solutions even for the NCERT questions.

He was born on January 2, 1946 in a village of Delhi. He graduated from Kirori Mal College, University of Delhi. After completing his M.Sc. in Mathematics in 1969, he joined N.A.S. College, Meerut, as a lecturer. In 1976, he was awarded a fellowship for 3 years and joined the University of Delhi for his Ph.D. Thereafter, he was promoted as a reader in N.A.S. College, Meerut. In 1999, he joined M.M.H. College, Ghaziabad, as a reader and took voluntary retirement in 2003. He has authored more than 75 titles ranging from Nursery to M. Sc. He has also written books for competitive examinations right from the clerical grade to the I.A.S. level.

FAQs

Why must I refer to the RS Aggarwal textbook?
RS Aggarwal is one of the most important reference books for high school grades and is recommended to every high school student. The book covers every single topic in detail. It goes in-depth and covers every single aspect of all the mathematics topics and covers both theory and problem-solving. The book is true of great help for every high school student. Solving a majority of the questions from the book can help a lot in understanding topics in detail and in a manner that is very simple to understand. Hence, as a high school student, you must definitely dwell your hands on RS Aggarwal!

Why should you refer to RS Aggarwal textbook solutions on Indcareer?
RS Aggarwal is a book that contains a few of the hardest questions of high school mathematics. Solving them and teaching students how to solve questions of such high difficulty is not the job of any neophyte. For solving such difficult questions and more importantly, teaching the problem-solving methodology to students, an expert teacher is mandatory!

Does IndCareer cover RS Aggarwal Textbook solutions for Class 6-12?
RS Aggarwal is available for grades 6 to 12 and hence our expert teachers have formulated detailed solutions for all the questions of each edition of the textbook. On our website, you’ll be able to find solutions to the RS Aggarwal textbook right from Class 6 to Class 12. You can head to the website and download these solutions for free. All the solutions are available in PDF format and are free to download!

Read More

• RS Aggarwal Solutions for Class 7 Maths Chapter 3–Decimals
• RS Aggarwal Solutions for Class 7 Maths Chapter 21–Collection and Organisation of Data (Mean, Median, and Mode)
• RD Sharma Solutions for Class 11 Maths Chapter 15–Linear Inequations
• RD Sharma Solutions for Class 6 Maths Chapter 9–Ratio, Proportion and Unitary Method
• NCERT Solutions for 6th Class Maths: Chapter 8-Decimals