Rs Aggrawal 2019 Solutions for Class 6 Math Chapter 7 Decimals are provided here with simple step-by-step explanations. These solutions for Decimals are extremely popular among Class 6 students for Math Decimals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggrawal 2019 Book of Class 6 Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggrawal 2019 Solutions. All Rs Aggrawal 2019 Solutions for class Class 6 Math are prepared by experts and are 100% accurate.

Page No 113:

Question 1:

Write each of the following in figures:
(i) Fifty-eight point six three
(ii) One hundred twenty-four point four two five
(iii) Seven point seven six
(iv) Nineteen point eight
(v) Four hundred four point zero four four
(vi) Point one seven three
(vii) Point zero one five

Answer:

(i) 58.63
(ii) 124.425
(iii) 7.76
(iv) 19.8
(v) 404.044
(vi) 0.173
(vii) 0.015

Page No 113:

Question 2:

Write the place value of each digit in each of the following decimals:
(i) 14.83
(ii) 275.269
(iii) 46.075
(iv) 302.459
(v) 5370.34
(vi) 186.209

Answer:

(i) In 14.83, we have:
Place value of 1 = 1 tens = 10
Place value of 4 = 4 ones = 4
Place value of 8 = 8 tenths = 810
Place value of 3 = 3 hundredths = 3100

(ii) In 275.269, we have:
Place value of 2 = 2 hundreds = 200
Place value of 7 = 7 tens = 70
Place value of 5 = 5 ones = 5
Place value of 2 = 2 tenths = 210
Place value of 6 = 6 hundredths = 6100
Place value of 9 = 9 thousandths = 91000

(iii) In 46.075, we have:
Place value of 4 = 4 tens = 40
Place value of 6 = 6 ones = 6
Place value of 0 = 0 tenths = 010= 0
Place value of 7 = 7 hundredths = 7100
Place value of 5 = 5 thousandths = 51000

(iv) In 302.459, we have:
Place value of 3 = 3 hundreds = 300
Place value of 0 = 0 tens = 0
Place value of 2 = 2 ones = 2
Place value of 4 = 4 tenths = 410
Place value of 5 = 5 hundredths = 5100
Place value of 9 = 9 thousandths = 91000

(v) In 5370.34, we have:
Place value of 5 = 5 thousands = 5000
Place value of 3 = 3 hundreds = 300
Place value of 7 = 7 tens = 70
Place value of 0 = 0 ones = 0
Place value of 3 = 3 tenths = 310
Place value of 4 = 4 hundredths = 4100

(vi) In 186.209, we have:
Place value of 1 = 1 hundreds = 100
Place value of 8 = 8 tens = 80
Place value of 6 = 6 ones = 6
Place value of 2 = 2 tenths = 210
Place value of 0 = 0 hundredths = 0
Place value of 9 = 9 thousandths = 91000

Page No 113:

Question 3:

Write each of the following decimals in expanded form:
(i) 67.83
(ii) 283.61
(iii) 24.675
(iv) 0.294
(v) 8.006
(vi) 4615.72

Answer:

(i) 67.83
 = 6 tens + 7 ones + 8 tenths + 3 hundredths
 = 60 + 7 + 810 + 3100

(ii) 283.61
 = 2 hundreds  + 8 tens + 3 ones + 6 tenths + 1 hundredths
 = 200 + 80 + 3 + 610  + 1100

(iii) 24.675
 = 2 tens + 4 ones + 6 tenths + 7 hundredths + 5 thousandths
 = 20 + 4 + 610 + 7100 + 51000

(iv) 0.294
 = 2 tenths + 9 hundredths + 4 thousandths
 = 210  + 9100 + 41000

(v) 8.006
 = 8 ones + 0 tenths + 0 hundredths  + 6 thousandths
 = 8 + 010 + 0100 + 61000

(vi) 4615.72
 = 4 thousands + 6 hundreds + 1 tens + 5 ones + 7 tenths + 2 hundredths
 = 4000 + 600 + 10 + 5 + 710 + 2100

Page No 113:

Question 4:

Write each of the following in decimals form:
(i) 40 + 6 + 710 + 9100
(ii) 500 + 70 + 8 + 310 + 1100 + 61000
(iii) 700 + 30 + 1 + 810 + 4100
(iv) 600 + 5 + 7100 + 91000
(v) 800 + 5 + 810 + 61000
(vi) 30 + 9 + 4100 + 81000

Answer:

(i) 40 + 6 + 710 + 9100 = 46 + 0.7 + .09 = 46.79

(ii) 500 + 70 + 8 + 310 + 1100 + 61000 = 578 + 0.3 + 0.01 + 0.006 = 578.316

(iii) 700 + 30 + 1 + 810 + 4100 = 731 + 0.8 + 0.04 = 731.84

(iv) 600 + 5 + 7100 + 91000 = 605 + 0.07 + 0.009 = 605.079

(v) 800 + 5 + 810 + 61000 = 805 + 0.8 + 0.006 = 805.806

(vi) 30 + 9 + 4100 + 81000 = 39 + 0.04 + 0.008 = 39.048



Page No 114:

Question 5:

Convert each of the following into like decimals:
(i) 7.5, 64.23, 0.074
(ii) 0.6, 5.937, 2.36, 4.2
(iii) 1.6, 0.07, 3.58, 2.9
(iv) 2.5, 0.63, 14.08, 1.637

Answer:

(i) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.
  7.5 = 7.500
64.23 = 64.230
0.074 = 0.074

(ii) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.
  0.6 = 0.600
5.937 = 5.937
2.36 = 2.360
4.2 = 4.200

(iii) Each of the numbers has maximum 2 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.
  1.6 = 1.60
0.07 = 0.07
3.58 = 3.58
2.9 = 2.90

(iv) Each of the numbers has maximum 3 decimal places. So, we convert them into numbers having three decimal places by annexing suitable number of zeroes to the extreme right of the decimal part.
  2.5 = 2.500
0.63 = 0.630
14.08 = 14.080
1.637 = 1.637

Page No 114:

Question 6:

Fill in each of the place holders with the correct symbol > or <:
(i) 84.23      76.35
(ii) 7.608      7.68
(iii) 8.34      8.43
(iv) 12.06      12.006
(v) 3.85      3.805
(vi) 0.97      1.07

Answer:

(i) 84.23 > 76.35
Since 84 is greater than 76, 84.23 is greater than 76.35. (Comparing the whole number parts)

(ii) 7.608 < 7.680
Since 8 is greater than 0 at the hundredths place, 7.608 is smaller than 7.680.

(iii) 8.34 < 8.43
Since 4 is greater than 3 at the tenths place, 8.34 is smaller than 8.43.

(iv) 12.06 > 12.006
Since 6 is greater than 0 at the hundredths place, 12.06 is greater than 12.006.

(v) 3.850 > 3.805
Since 5 is greater than 0 at the hundredths place, 3.850 is greater than 3.805.

(vi) 0.97 < 1.07
Since 1 is greater than 0, 0.97 is smaller than 1.07. (Comparing the whole number parts)

Page No 114:

Question 7:

Arrange the following decimals in ascending order:
(i) 5.8, 7.2, 5.69, 7.14, 5.06
(ii) 0.6, 6.6, 6.06, 66.6, 0.06
(iii) 6.54, 6.45, 6.4, 6.5, 6.05
(iv) 3.3, 3.303, 3.033, 0.33, 3.003

Answer:

(i) 5.8, 7.2, 5.69, 7.14, 5.06
 Converting the given decimals into like decimals:
    5.80, 7.20, 5.69, 7.14, 5.06
  Clearly, 5.06 < 5.69 < 5.80 < 7.14 < 7.20
  Hence, the given decimals can be arranged in the ascending order as follows:
          5.06, 5.69, 5.80, 7.14 and 7.2

(ii) 0.6, 6.6, 6.06, 66.6, 0.06
  Converting the given decimals into like decimals:
   0.60, 6.60, 6.06, 66.60, 0.06
  Clearly, 0.06 < 0.60 < 6.06 < 6.60 < 66.60
  Hence, the given decimals can be arranged in the ascending order as follows:
           0.06, 0.60, 6.06, 6.60 and 66.60

(iii) 6.54, 6.45, 6.4, 6.5, 6.05
Converting the given decimals into like decimals:
  6.54, 6.45, 6.40, 6.50, 6.05
  Clearly, 6.05 < 6.40 < 6.45 < 6.50 < 6.54
  Hence, the given decimals can be arranged in the ascending order as follows:
         6.05, 6.40, 6.45, 6.50 and 6.54

(iv) 3.3, 3.303, 3.033, 0.33, 3.003
Converting the given decimals into like decimals:
  3.300, 3.303, 3.033, 0.330, 3.003
  Clearly, 0.330 < 3.003 < 3.033 < 3.300 < 3.303
  Hence, the given decimals can be arranged in the ascending order as follows:
         0.33, 3.003, 3.033, 3.300 and 3.303

Page No 114:

Question 8:

Arrange the following decimals in descending order:
(i) 7.3, 8.73, 73.03, 7.33, 8.073
(ii) 3.3, 3.03, 30.3, 30.03, 3.003
(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007
(iv) 8.88, 8.088, 88.8, 88.08, 8.008

Answer:

(i) 7.3, 8.73, 73.03, 7.33, 8.073
 Converting each decimal into like decimals:
  7.300, 8.730, 73.030, 7.330, 8.073
 Clearly, 73.030 > 8.730 > 8.073 > 7.330 > 7.300
 Hence, the given decimals can be arranged in the descending order as follows:
   73.03, 8.73, 8.073, 7.33 and 7.3

(ii) 3.3, 3.03, 30.3, 30.03, 3.003
 Converting each decimal into like decimals:
   3.300, 3.030, 30.300, 30.030, 3.003
 Clearly, 30.300 > 30.030 > 3.300 > 3.030 > 3.003
 Hence, the given decimals can be arranged in the descending order as follows:
   30.3, 30.03, 3.3, 3.03 and 3.003

(iii) 2.7, 7.2, 2.27, 2.72, 2.02, 2.007
 Converting each decimal into like decimals:
   2.700, 7.200, 2.270, 2.720, 2.020, 2.007
 Clearly, 7.200 > 2.720 > 2.700 > 2.270 > 2.020 > 2.007
 Hence, the given decimals can be arranged in the descending order as follows:
      7.2, 2.72, 2.7, 2.27, 2.02 and 2.007

(iv) 8.88, 8.088, 88.8, 88.08, 8.008
 Converting each decimal into like decimals:
        8.880, 8.088, 88.800, 88.080, 8.008
 Clearly, 88.800 > 88.080 > 8.880 > 8.088 > 8.008
 Hence, the given decimals can be arranged in the descending order as follows:
        88.8, 88.08, 8.88, 8.088 and 8.008



Page No 118:

Question 1:

Convert each of the following into a fraction in its simplest form:
.9

Answer:

We have:
 .9 = 910

Page No 118:

Question 2:

Convert each of the following into a fraction in its simplest form:
0.6

Answer:

We have:
 0.6 = 610 = 35

Page No 118:

Question 3:

Convert each of the following into a fraction in its simplest form:
.08

Answer:

We have:
 0.08 = 8100 = 450 = 225
    

Page No 118:

Question 4:

Convert each of the following into a fraction in its simplest form:
0.15

Answer:

We have:
 0.15 = 15100 = 320

Page No 118:

Question 5:

Convert each of the following into a fraction in its simplest form:
0.48

Answer:

We have:
 0.48 = 48100 = 1225

Page No 118:

Question 6:

Convert each of the following into a fraction in its simplest form:
.053

Answer:

We have:
 0.053 = 531000 

Page No 118:

Question 7:

Convert each of the following into a fraction in its simplest form:
0.125

Answer:

We have:
 0.125 = 1251000 = 25200 =540= 18

Page No 118:

Question 8:

Convert each of the following into a fraction in its simplest form:
.224

Answer:

We have:
0.224 = 2241000 = 56250 = 28125

Page No 118:

Question 9:

Convert each of the following as a mixed-fraction:
6.4

Answer:

We have:
 6.4 = 6410 = 325 = 625

Page No 118:

Question 10:

Convert each of the following as a mixed-fraction:
16.5

Answer:

We have:
 16.5 = 16510 = 332 =1612

Page No 118:

Question 11:

Convert each of the following as a mixed-fraction:
8.36

Answer:

We have:
 8.36 = 836100 = 20925 = 8925

Page No 118:

Question 12:

Convert each of the following as a mixed-fraction:
4.275

Answer:

We have:
 4.275 = 42751000 = 17140 = 41140

Page No 118:

Question 13:

Convert each of the following as a mixed-fraction:
25.06

Answer:

We have:
 25.06 = 2506100 = 125350 =25350

Page No 118:

Question 14:

Convert each of the following as a mixed-fraction:
7.004

Answer:

We have:
7.004 = 70041000 = 1751250 = 71250

Page No 118:

Question 15:

Convert each of the following as a mixed-fraction:
2.052

Answer:

We have:
2.052 = 20521000 = 513250 = 213250

Page No 118:

Question 16:

Convert each of the following as a mixed-fraction:
3.108

Answer:

We have:
3.108 = 31081000 = 777250 = 327250

Page No 118:

Question 17:

Convert each of the following into a decimal:
2310

Answer:

We have:
2310 = 2310 = 2 + 0.3 = 2.3

Page No 118:

Question 18:

Convert each of the following into a decimal:
167100

Answer:

We have:
167100 = 167100 = 1 + 0.67 = 1.67

Page No 118:

Question 19:

Convert each of the following into a decimal:
1589100

Answer:

We have:
1589100 = 1589100 = 15+ 0.89 = 15.89

Page No 118:

Question 20:

Convert each of the following into a decimal:
54131000

Answer:

We have:
54131000 = 54131000 = 5 + 0.413 = 5.413

Page No 118:

Question 21:

Convert each of the following into a decimal:
214151000

Answer:

We have:
214151000 = 214151000 = 21 + 0.415 = 21.415

Page No 118:

Question 22:

Convert each of the following into a decimal:
254

Answer:


We have:
254 = 614 = 6 + 0.25 = 6.25

Page No 118:

Question 23:

Convert each of the following into a decimal:
335

Answer:


We have:
335= 3 + 0.6 = 3.6

Page No 118:

Question 24:

Convert each of the following into a decimal:
1425

Answer:


We have:
 1425 = 1 + 0.16 = 1.16

Page No 118:

Question 25:

Convert each of the following into a decimal:
51750

Answer:



We have:
51750 = 5 + 0.34 = 5.34

Page No 118:

Question 26:

Convert each of the following into a decimal:
1238

Answer:


We have:
1238 = 12 + 0.375 = 12.375

Page No 118:

Question 27:

Convert each of the following into a decimal:
21940

Answer:



We have:
21940 = 2 + 0.475 = 2.475

Page No 118:

Question 28:

Convert each of the following into a decimal:
1920

Answer:


We have:
1920 = 0.95

Page No 118:

Question 29:

Convert each of the following into a decimal:
3750

Answer:


We have:
3750 =  0.74

Page No 118:

Question 30:

Convert each of the following into a decimal:
107250

Answer:


We have:
107250 = 0.428

Page No 118:

Question 31:

Convert each of the following into a decimal:
340

Answer:


We have:
340 = 0.075

Page No 118:

Question 32:

Convert each of the following into a decimal:
78

Answer:


We have:
78 = 0.875

Page No 118:

Question 33:

Using decimals, express
(i) 8 kg 640 g in kilograms
(ii) 9 kg 37 g in kilograms
(iii) 6 kg 8 g in kilograms

Answer:

(i) 8 kg 640 g in kilograms:
     8 kg + 640 gm = 8 kg + 6401000 kg
     8 kg + 0.640 kg = 8.640 kg

(ii) 9 kg 37 g in kilograms:
     9 kg + 37 gm = 9 kg + 371000 kg
     9 kg + 0.037 kg = 9.037 kg

(iii) 6 kg 8 g in kilograms:
      6 kg + 8 gm = 6 kg + 81000 kg
      6 kg + 0.008 kg = 6.008 kg

Page No 118:

Question 34:

Using decimals, express
(i) 4 km 365 m in kilometres
(ii) 5 km 87 m in kilometres
(iii) 3 km 6 m in kilometres
(iv) 270 m in kilometres
(v) 35 m in kilometres
(vi) 6 m in kilometres

Answer:

(i) 4 km 365 m in kilometres:
    4 km + 365 m = 4 km + 3651000 km     [Since 1 km = 1000 m]
    4 km + 0.365 km = 4.365 km

(ii) 5 km 87 m in kilometres:
    5 km + 87 m = 5 km + 871000 km     [Since 1 km = 1000 m]
    5 km + 0.087 km = 5.087 km

(iii) 3 km 6 m in kilometres:
     3 km + 6 m = 3 km + 61000 km      [Since 1 km = 1000 m]
     3 km + 0.006 km = 3.006 km

(iv) 270 m in kilometres:
      2701000 km = 0.270 km                     [Since 1 km = 1000 m]

(v) 35 m in kilometres:
      351000 km = 0.035 km                      [Since 1 km = 1000 m]

(vi) 6 m in kilometres:
       61000 km = 0.006 km                    [Since 1 km = 1000 m]

Page No 118:

Question 35:

Using decimals, express
(i) 15 kg 850 g in kilograms
(ii) 8 kg 96 g in kilograms
(iii) 540 g in kilograms
(iv) 8 g in kilograms

Answer:

(i) 15 kg 850 g in kilograms:
    15 kg + 850 gm = 15 kg + 8501000 kg        [Since 1 kg = 1000 gm]
    15 kg + 0.850 kg = 15.850 kg

(ii) 8 kg 96 g in kilograms:
     8 kg + 96 gm = 8 kg + 961000 kg         [Since 1 kg = 1000 gm]
     8 kg + 0.096 kg = 8.096 kg

(iii) 540 g in kilograms:
       540 gm = 5401000 kg = 0.540 kg        [Since 1 kg = 1000 gm]

(iv) 8 g in kilograms:
       8 gm = 81000 kg = 0.008 kg           [Since 1 kg = 1000 gm]

Page No 118:

Question 36:

Using decimals, express
(i) Rs 18 and 25 paise in rupees
(ii) Rs 9 and 8 paise in rupees
(iii) 32 paise in rupees
(iv) 5 paise in rupees

Answer:

(i) Rs 18 and 25 paise in rupees:
    Rs 18 + 25 paise = Rs 18 + Rs 25100         [Since Re 1 = 100 paise]
    Rs 18 + Rs 0.25 = Rs 18.25

(ii) Rs 9 and 8 paise in rupees:
    Rs 9 + 8 paise = Rs 9 + Rs 8100         [Since Re 1 = 100 paise]
    Rs 9 + Rs 0.08 = Rs 9.08

(iii) 32 paise in rupees:
      32 paise = Rs 32100 = Rs 0.32          [Since Re 1 = 100 paise]

(iv) 5 paise in rupees:
      5 paise = Rs 5100 = Rs 0.05          [Since Re 1 = 100 paise]



Page No 120:

Question 1:

Add the following decimals:
9.6, 14.8, 37 and 5.9

Answer:

9.6, 14.8, 37 and 5.9
Converting the decimals into like decimals:
9.6, 14.8, 37.0 and 5.9
Let us write the given numbers in the column form.
Now, adding:
     9.6
   14.8
   37.0
     5.9
   67.3
Hence, the sum of the given numbers is 67.3.

Page No 120:

Question 2:

Add the following decimals:
23.7, 106.94, 68.9 and 29.5

Answer:

23.7, 106.94, 68.9 and 29.5
Converting the decimals into like decimals:
23.70, 106.94, 68.90 and 29.50
Let us write the given numbers in the column form.
Now, adding:
   23.70
 106.94
  68.90
  29.50
 229.04
Hence, the sum of the given numbers is 229.04.

Page No 120:

Question 3:

Add the following decimals:
72.8, 7.68, 16.23 and 0.7

Answer:

72.8, 7.68, 16.23 and 0.7
Converting the decimals into like decimals:
72.80, 7.68, 16.23 and 0.70
Let us write the given numbers in the column form.
Now, adding:
   72.80
     7.68
   16.23
     0.70
   97.41
Hence, the sum of the given numbers is 97.41.

Page No 120:

Question 4:

Add the following decimals:
18.6, 84.75, 8.345 and 9.7

Answer:

18.6, 84.75, 8.345 and 9.7
Converting the decimals into like decimals:
18.600, 84.750, 8.345 and 9.700
Let us write the given numbers in the column form.
Now, adding:
   18.600
   84.750
     8.345
     9.700
  121.395
Hence, the sum of the given numbers is 121.395.

Page No 120:

Question 5:

Add the following decimals:
8.236, 16.064, 63.8 and 27.53

Answer:

8.236, 16.064, 63.8 and 27.53
Converting the decimals into like decimals:
8.236, 16.064, 63.800 and 27.530
Let us write the given numbers in the column form.
Now, adding:
     8.236
   16.064
   63.800
   27.530  
  115.630
Hence, the sum of the given numbers is 115.630.

Page No 120:

Question 6:

Add the following decimals:
28.9, 19.64, 123.697 and 0.354

Answer:

28.9, 19.64, 123.697 and 0.354
Converting the decimals into like decimals:
28.900, 19.640, 123.697 and 0.354
Let us write the given numbers in the column form.
Now, adding:
    28.900
    19.640
  123.697
     0.354 
  172.591
Hence, the sum of the given numbers is 172.591.

Page No 120:

Question 7:

Add the following decimals:
4.37, 9.638, 17.007 and 6.8

Answer:

4.37, 9.638, 17.007 and 6.8
Converting the decimals into like decimals:
4.370, 9.638, 17.007 and 6.800
Let us write the given numbers in the column form.
Now, adding:
    4.370
    9.683
  17.007
    6.800 
  37.815  
Hence, the sum of the given numbers is 37.815.

Page No 120:

Question 8:

Add the following decimals:
14.5, 0.038, 118.573 and 6.84

Answer:

14.5, 0.038, 118.573 and 6.84
Converting the decimals into like decimals:
14.500, 0.038, 118.573 and 6.840
Let us write the given numbers in the column form.
Now, adding:
   14.500
     0.038
  118.573
     6.840 
  139.951 
Hence, the sum of the given numbers is 139.951.

Page No 120:

Question 9:

During three days of a week, a rickshaw puller earns Rs 32.60, Rs 56.80 and Rs 72 respectively. What is his total earning during these days?

Answer:

Earning on the 1st day of the week =  Rs 32.60
Earning on the 2nd day of the week = Rs 56.80
Earning on the 3rd day of the week = Rs 72.00
Total earning =                                 Rs 161.40

Page No 120:

Question 10:

A man purchases an almirah for Rs 11025, gives Rs 172.50 as its cartage and spends Rs 64.80 on its repair. How much does the almirah cost him?

Answer:

Cost of the almirah =          Rs 11025.00
Money spent on cartage =       Rs 172.50
Money spent on repair =           Rs 64.800
Total cost of the almirah =  Rs 11262.3    

Page No 120:

Question 11:

Ramesh covers 36 km 235 m by taxi, 4 km 85 m by rickshaw and 1 km 80 m on foot What is the total distance covered by him?

Answer:

Distance covered by the taxi =        36 km 235 m
Distance covered by the rickshaw =  4 km 085 m
Distance covered on foot =               1 km 080 m
Total distance covered =                41 km  400 m

Page No 120:

Question 12:

A bag contains 45 kg 80 g of sugar and the mass of the empty bag is 950 g. What is the mass of the bag containing this much of sugar?

Answer:

Weight of sugar in the bag =   45 kg 080 g
Weight of the empty bag =       0 kg 950 g
Total weight of the bag =         46 kg 030 g

Page No 120:

Question 13:

Ramu bought 2 m 70 cm cloth for his shirt and 2 m 60 cm cloth for his pyjamas. Find the total length of cloth bought by him.

Answer:

Length of cloth for his shirt =         2 m 70 cm
Length of cloth for his pyjamas =    2 m 60 cm
Total length of cloth bought =         5 m 30 cm

Page No 120:

Question 14:

Radhika bought 2 m 5 cm cloth for her salwar and 3 m 35 cm cloth for her shirt. Find the total length of cloth bought by her.

Answer:

Length of cloth for her salwar =        2 m 05 cm
Length of cloth for her shirt =           3 m 35 cm
Total length of cloth bought =           5 m 40 cm



Page No 122:

Question 1:

Subtract:
27.86 from 53.74

Answer:

Let us write the numbers in the column form with the larger one at the top.
Now, subtracting:
   53.74
 - 27.86
   25.88
 53.74 - 27.86 = 25.88

Page No 122:

Question 2:

Subtract:
64.98 from 103.87

Answer:

Let us write the numbers in the column form with the larger one at the top.
Now, subtracting:
 103.87
- 64.98
  38.89
103.87 - 64.98 = 38.89

Page No 122:

Question 3:

Subtract:
59.63 from 92.4

Answer:

Converting the given numbers into like decimals:
59.63 and 92.40
Let us write them in the column form with the larger number at the top.
Now, subtracting:
   92.40
 - 59.63
   32.77
53.74 - 27.86 = 32.77

Page No 122:

Question 4:

Subtract:
56.8 from 204

Answer:

Converting the given numbers into like decimals:
56.80 and 204.00
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  204.00
 - 56.80
   147.2
204.00 - 56.80 = 147.2

Page No 122:

Question 5:

Subtract:
127.38 from 216.2

Answer:

Converting the given numbers into like decimals:
127.38 and 216.20
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  216.20
- 127.38
    88.82
 216.20 - 127.38 = 88.82

Page No 122:

Question 6:

Subtract:
39.875 from 70.68

Answer:

Converting the given numbers into like decimals:
39.875 and 70.680
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  70.680
- 39.875
  30.805
70.680 - 39.875 = 30.805

Page No 122:

Question 7:

Subtract:
348.237 from 523.12

Answer:

Converting the given numbers into like decimals:
348.237 and 523.120
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  523.120
- 348.237
  174.883
523.120 - 348.237 = 174.883

Page No 122:

Question 8:

Subtract:
458.573 from 600

Answer:

Converting the given numbers into like decimals:
458.573 and 600.000
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  600.000
- 458.573
  141.427
600.000 - 458.573 =141.427

Page No 122:

Question 9:

Subtract:
149.456 from 206.321

Answer:

Let us write the numbers in the column form with the larger one at the top.
Now, subtracting:
  206.321
- 149.456
    56.865
 206.321 - 149.456 = 56.865

Page No 122:

Question 10:

Subtract:
0.612 from 3.4

Answer:

Converting the given numbers into like decimals:
3.400 and 0.612
Let us write them in the column form with the larger number at the top.
Now, subtracting:
  3.400
- 0.612
  2.788
3.400 - 0.612 = 2.788

Page No 122:

Question 11:

Simplify:
37.6 + 72.85 − 58.678 − 6.09

Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:
                         
        37.60                        58.678
     + 72.85                      +  6.090                
       110.45                        64.768 
                         
                                 
                                      110.450
                                   -  64.768
                                        45.682    

(37.60 + 72.85) - (58.678 + 6.090)
= 110.450 - 64.768
= 45.682                     

Page No 122:

Question 12:

Simplify:
75.3 − 104.645 + 178.96 − 47.9

Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:
                         
      178.96                        104.645
     + 75.30                      + 47.900              
      254.26                        152.545

(75.30 + 178.96) - (104.645 + 47.900)
254.260 - 152.545
101.715                           254.260
                                   - 152.545
                                       101.715
                                 
                              

Page No 122:

Question 13:

Simplify:
213.4 − 56.84 − 11.87 − 16.087

Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:
                         
       56.840
       11.870                     
     +16.087                                  
       84.797                 

(213.400) - (56.840 + 11.870 + 16.087)
213.400 - 84.797
128.603                          213.400
                                   -  84.797
                                      128.603
                                 
                              

Page No 122:

Question 14:

Simplify:
76.3 − 7.666 − 6.77

Answer:

Converting the given decimals into like decimals, then adding and, finally, subtracting:
                         
         7.666                       
     +  6.770                            
       14.436                   

(76.300) - (7.666 + 6.770)
= 76.300 - 14.436
= 61.864                          

  76.300
-14.436
 61.864
                                 
                              

Page No 122:

Question 15:

What is to be added to 74.5 to get 91?

Answer:

In order to get the number that must be added to 74.5 to get 91, we must subtract 74.5 from 91.0.

         91.0
    -  74.5
         16.5

Thus, 16.5 is the required number.

Page No 122:

Question 16:

What is to be subtracted from 7.3 to get 0.862?

Answer:

In order to get the number that must be subtracted from 7.300 to get .0862, we have to subtract 0.862 from 7.300.

         7.300
    -  0.862
        6.438 

Thus, 6.438 is the required number.

Page No 122:

Question 17:

By how much should 23.754 be increased to get 50?

Answer:

In order to get the number by which 23.754 must be increased to get 50, we have to subtract 23.754 from 50.000.
 
      50.000
   -23.754
      26.246

Page No 122:

Question 18:

By how much should 84.5 be decreased to get 27.84?

Answer:

In order to get the number by which 84.50 must be decreased to get 27.84, we have to subtract 27.84 from 84.50.
 
      84.50
   -27.84
      56.66

Page No 122:

Question 19:

If the school bags of Neelam and Garima weigh 6 kg 80 g and 5 kg 265 g respectively, whose bag is heavier and by how much?

Answer:

Weight of Neelam's school bag =       6080 g  {Converting into grams: 6 kg + 80 g = (6000 + 80) g =  6080 g}
Weight of Garima's school bag =     -5265 g  {Converting into grams: 5 kg + 265 g = (5000 + 265)g = 5265 g}
Difference of the weights of bags =      815 g
Thus, the weight of Neelam's school bag is more than that of Garima's school bag by 815 grams, i.e. by 0.815 kg.

Page No 122:

Question 20:

Kunal purchased a notebook for Rs 19.75, a pencil for Rs 3.85 and a pen for Rs 8.35 from a book shop. He gave a 50-rupee note to the shopkeeper. What amount did he get back?

Answer:

Cost of the notebook =  Rs 19.75
Cost of the pencil =        Rs 3.85
Cost of the pen =        + Rs 8.35
Total cost payable =      Rs 31.95

Total money paid =      Rs 50.00
Total money spent = -Rs 31.95
Balance =                   Rs 18.05 

Thus, Kunal got back Rs 18.05 from the shopkeeper.

Page No 122:

Question 21:

Sunita purchased 5 kg 75 g of fruits and 3 kg 465 g of vegetables, and put them in a bag. If this bag with these contents weighs 9 kg, find the weight of the empty bag.

Answer:

Weight of the fruits =                                  5 kg 075 g
Weight of the vegetables =                       + 3 kg 465 g
Total weight of the contents of the bag =      8 kg 540 g

Total weight of the bag with its contents =    9 kg 000 g
Total weight of the contents of the bag =  - 8 kg 540 g
Weight of the empty bag =                           0 kg 460 g
Thus, the weight of the empty bag is 460 grams.



Page No 123:

Question 22:

The distance between Reeta's house and her office is 14 km. She covers 10 km 65 m by scooter, 3 km 75 m by bus and the rest on foot. How much distance does she cover by walking?

Answer:

Converting into metres:
10 km 65 m = (10 + 0.065) m = 10.065 m
3 km 75 m = (3 + 0.075) m = 3.075 m

Distance covered by the scooter =                             10.065 km
Distance covered by the bus =                                 + 3.075 km
Total distance covered by the bus and the scooter =   13.140 km

Total distance between the house and the office =       14.000 km
Total distance covered by the bus and the scooter = -13.140 km
Distance covered on foot =                                          0.860 km

Distance covered by walking = 0.860 km = 860 metres

Page No 123:

Question 1:

Mark (✓) against the correct answer in each of the following:
710=?
(a) 7.1
(b) 1.7
(c) 0.7
(d) 0.07

Answer:

(c) 0.7

710 = 7 tenths = 0.7

Page No 123:

Question 2:

Mark (✓) against the correct answer in each of the following:
5100=?
(a) 5.1
(b) 5.01
(c) 0.5
(d) 0.05

Answer:

(d) 0.05
 5100 = 5 hundredths = 0.05

Page No 123:

Question 3:

Mark (✓) against the correct answer in each of the following:
91000=?
(a) 0.0009
(b) 0.009
(c) 9.001
(d) none of these

Answer:

(b) 0.009
91000 = 9 thousandths = 0.009

Page No 123:

Question 4:

Mark (✓) against the correct answer in each of the following:
161000=?
(a) 0.016
(b) 0.16
(c) 0.0016
(d) 1.006

Answer:

(a) 0.016
161000 = 16 thousandths = 0.016

Page No 123:

Question 5:

Mark (✓) against the correct answer in each of the following:
1341000=?
(a) 13.4
(b) 1.34
(c) 0.134
(d) 0.0134

Answer:

(c) 0.134
 1341000 = 134 thousandths = 0.134

Page No 123:

Question 6:

Mark (✓) against the correct answer in each of the following:
217100=?
(a) 2.17
(b) 2.017
(c) 0.217
(d) 21.7

Answer:

(a) 2.17
 217100 = 2 + 17100 = 2 + 0.17 = 2.17

Page No 123:

Question 7:

Mark (✓) against the correct answer in each of the following:
43100=?
(a) 4.3
(b) 4.03
(c) 4.003
(d) 43.10

Answer:

(b) 4.03
 43100 = 4 + 3100 = 4 + 0.03 = 4.03

Page No 123:

Question 8:

Mark (✓) against the correct answer in each of the following:
6.25 = ?
(a) 612
(b) 614
(c) 6212
(d) none of these

Answer:

b) 614614
6.25 = 6 + 0.25 = 6 + 25100 = 6 + 14 = 614

Page No 123:

Question 9:

Mark (✓) against the correct answer in each of the following:
625=?
(a) 2.4
(b) 0.24
(c) 0.024
(d) none of these

Answer:

(b) 0.24
     625 =  0.24
                                  
            25) 60 (0.24
               -50
                  100
              - 100
                   0  

Page No 123:

Question 10:

Mark (✓) against the correct answer in each of the following:
478=?
(a) 4.78
(b) 4.87
(c) 4.875
(d) none of these

Answer:

(c) 4.875
478 =  4 + 78 = 4 + 0.875 = 4.875

Page No 123:

Question 11:

Mark (✓) against the correct answer in each of the following:
24.8 = ?
(a) 2445
(b) 2425
(c) 2415
(d) none of these

Answer:

(a)  2445
24.8 = 24 + 0.8 = 24 + 810 = 24 + 45 = 2445



Page No 124:

Question 12:

Mark (✓) against the correct answer in each of the following:
2125=?
(a) 2.4
(b) 2.04
(c) 2.004
(d) none of these

Answer:

(b) 2.04
2125 = 2 + 125 = 2 + 0.04 = 2.04

Page No 124:

Question 13:

Mark (✓) against the correct answer in each of the following:
2+310+4100
(a) 2.304
(b) 2.403
(c) 2.34
(d) none of these

Answer:

(c) 2.34
2 + 310 + 4100 = 2 + 0.3 + 0.04 = 2.34

Page No 124:

Question 14:

Mark (✓) against the correct answer in each of the following:
2+6100=?
(a) 2.006
(b) 2.06
(c) 2.6
(d) none of these

Answer:

(b) 2.06
2 + 6100 = 2 + 0.06 = 2.06

Page No 124:

Question 15:

Mark (✓) against the correct answer in each of the following:
4100+710000=?
(a) 0.47
(b) 0.407
(c) 0.0407
(d) none of these

Answer:

(c) 0.0407
4100 + 710000 = 0.04 + 0.0007 = 0.0407

Page No 124:

Question 16:

The correct expanded from of 2.06 is
(a) 2 × 10 + 6 × 110
(b) 2 × 1 + 6 ×110
(c) 2 × 1 + 6 × 1100
(d) none of these

Answer:

(c) (2 × 1) + (6 × 1100)

2.06 =  2 + 6100 = (2 × 1) + (6 × 1100)2 × 1) + (6 × 1(2 × 1) + (6 (2 × 1) + (6 

Page No 124:

Question 17:

Amoung 2.6, 2.006, 2.66 and 2.08, the largest number is
(a) 2.006
(b) 2.08
(c) 2.6
(d) 2.66

Answer:

(d) 2.66
Converting the given decimals into like decimals:
2.600, 2.006, 2.660 and 2.080
Among the given decimals, 2.660 is the largest.

Page No 124:

Question 18:

Which of the following is the correct order?
(a) 2.2 < 2.02 < 2.002 < 2.222
(b) 2.002 < 2.02 < 2.2 < 2.222
(c) 2.02 < 2.22 < 2.002 < 2.222
(d) none of these

Answer:

(b) 2.002 < 2.02 < 2.2 < 2.222

Converting the given decimals into like decimals:
2.002, 2.020, 2.200, 2.222

2.002 < 2.02 < 2.2 < 2.222

Page No 124:

Question 19:

Which is larger: 2.1 or 2.055?
(a) 2.1
(b) 2.055
(c) cannot be compared

Answer:

(a) 2.1
If we convert the given decimals into like decimals, we get 2.100 and 2.055.
At tenths place, 1 is greater than 0. Thus, 2.100 is greater than 2.055.

Page No 124:

Question 20:

Mark (✓) against the correct answer in each of the following:
1 cm = ?
(a) 0.1 m
(b) 0.01 m
(c) 0.001 m
(d) none of these

Answer:

(b) 0.01 m
1 m = 100 cm
1 cm = 1100m = 0.01 m   

Page No 124:

Question 21:

Mark (✓) against the correct answer in each of the following:
2 m 5 cm = ?
(a) 2.5 m
(b) 2.05 m
(c) 2.005 m
(d) 0.25 m

Answer:

(b) 2.05 m
2 m 5 cm = (2 + 5100) m = (2 + 0.05) m = 2.05 m

Page No 124:

Question 22:

Mark (✓) against the correct answer in each of the following:
2 kg 8 g = ?
(a) 2.8 kg
(b) 2.08 kg
(c) 2.008 kg
(d) none of these

Answer:

(c) 2.008 kg
1 kg = 1000 g
2 kg 8 g = 2 kg + 81000 kg = (2 + 0.008) kg = 2.008 kg

Page No 124:

Question 23:

Mark (✓) against the correct answer in each of the following:
2 kg 56 g = ?
(a) 2.56 kg
(b) 2.056 kg
(c) 2.560 kg
(d) none of these

Answer:

(b) 2.056 kg
2 kg + 56 g = (2 + 561000) kg = (2 + 0.056) kg = 2.056 kg

Page No 124:

Question 24:

Mark (✓) against the correct answer in each of the following:
2 km 35 m = ?
(a) 2.35 km
(b) 2.350 km
(c) 2.035 km
(d) none of these

Answer:

(c) 2.035 km
1 km = 1000 m
2 km 35 m  = (2 + 351000) km = (2 + 0.035) km = 2.035 km

Page No 124:

Question 25:

Mark (✓) against the correct answer in each of the following:
0.4 + 0.004 + 4.4 = ?
(a) 4.444
(b) 5.2
(c) 4.804
(d) 5.404

Answer:

(c) 4.804
0.4 + 0.004 + 4.4
Converting into like decimals and then adding:
   4.400
   0.004
+ 0.400
   4.804

Page No 124:

Question 26:

Mark (✓) against the correct answer in each of the following:
3.5 + 4.05 − 6.005 = ?
(a) 1.545
(b) 1.095
(c) 1.6
(d) none of these

Answer:

(a) 1.545
Converting into like decimals:
3.500 + 4.050 − 6.005
   3.500
+ 4.050
   7.550

   7.550
6.005
   1.545

Page No 124:

Question 27:

Mark (✓) against the correct answer in each of the following:
6.3 − 2.8 = ?
(a) 0.35
(b) 3.5
(c) 3.035
(d) none of these

Answer:

(b) 3.5

   6.3
2.8
   3.5

Page No 124:

Question 28:

Mark (✓) against the correct answer in each of the following:
5.01 − 3.6 = ?
(a) 4.65
(b) 1.95
(c) 1.41
(d) none of these

Answer:

(c) 1.41
Converting into like decimals and then subtracting:
   5.01
3.60
   1.41



Page No 125:

Question 29:

Mark (✓) against the correct answer in each of the following:
2 − 0.7 = ?
(a) 1.3
(b) 1.5
(c) 2.03
(d) none of these

Answer:

(a) 1.3
Converting into like decimals and then subtracting:
   2.0
0.7
   1.3

Page No 125:

Question 30:

Mark (✓) against the correct answer in each of the following:
1.1 − 0.3 = ?
(a) 0.8
(b) 0.08
(c) 8
(d) none of these

Answer:

(a) 0.8
Converting into like decimals and then subtracting:
   1.1
0.3
   0.8



Page No 126:

Question 1:

Convert 458 into a decimal fraction.

Answer:

458 = 4 + 58 =  4 + 0.625 = 4.625

Page No 126:

Question 2:

Express 105 cm into metres using decimals.

Answer:

1 cm = 1100 m
105 cm = 105100 m = (1 + 5100) m = (1 + 0.05) m = 1.05 m

Page No 126:

Question 3:

Express 6 km 5 m as km using decimals.

Answer:

1 m = 11000 km
  5 m = 51000 km = 0.005 km
6 km 5 m = (6 + 0.005) km = 6.005 km

Page No 126:

Question 4:

Express 8 m as kilometre using decimals.

Answer:

1 m = 11000 km
8 m = 81000 km = 0.008 km

Page No 126:

Question 5:

Add 26.4, 163.05, 8.75 and 5.6.

Answer:

Converting into like decimals and then adding:
    26.40
  163.05
     8.75
+   5.60
  203.80

Page No 126:

Question 6:

Subtract 0.528 from 3.2.

Answer:

Converting into like decimals and then subtracting:
    3.200
- 0.528
    2.672

Page No 126:

Question 7:

What is to be added to 63.5 to get 71?

Answer:

We subtract 63.5 from 71 in order to find the number that is to be added to 63.5 to make it 71.
    Converting into like decimals and then subtracting:  
     71.0
 - 63.5
      7.5

Page No 126:

Question 8:

What is to be subtracted from 13 to get 5.4?

Answer:

We subtract 5.4 from 13 in order to find the number that is to be subtracted from 13 to get 5.4.
Converting into like decimals and then subtracting:
      13.0
   -  5.4
       7.6 
Thus, we need to subtract 7.6 from 13 to get 5.4.

Page No 126:

Question 9:

Arrange the following decimals in descending order:
6.5, 6.05, 6.54, 6.4 and 6.45

Answer:

6.5, 6.05, 6.54, 6.4 and 6.45
Converting into like decimals:
6.50, 6.05, 6.54, 6.40 and 6.45
Clearly, 6.54 > 6.50 > 6.45 > 6.40 > 6.05
Hence, the given decimals can be arranged in the descending order in the following manner:
 6.54, 6.50, 6.45, 6.40 and 6.05

Page No 126:

Question 10:

Convert each of the following into a fraction in simplest form:
(i) .4
(ii) .35
(c) 0.08
(iv) 0.075

Answer:

(i) 0.4 = 410 = 25

(ii) 0.35 = 35100 = 720

(iii) 0.08 = 8100 = 225

(iv) 0.075 = 751000 = 340

Page No 126:

Question 11:

Mark (✓) against the correct answer in each of the following:
325=?
(a) 1.2
(b) 0.12
(c) 0.012
(d) none of these

Answer:

(b) 0.12
 325 = 0.12
                  
      25)  30 (0.12
         - 25
               50
           - 50  
                 0  

Page No 126:

Question 12:

Mark (✓) against the correct answer in each of the following:
61000=?
(a) 6.001
(b) 0.0006
(c) 0.006
(d) 0.06

Answer:

(c) 0.006
 61000 = 6 thousandths = 0.006

Page No 126:

Question 13:

Mark (✓) against the correct answer in each of the following:
23100=?
(a) 2.003
(b) 2.03
(c) 2.3
(d) none of these

Answer:

(b) 2.03
23100 = 2 + 3100 = 2 + 0.03 = 2.03

Page No 126:

Question 14:

Mark (✓) against the correct answer in each of the following:
The place value of 3 in 16.534 is
(a) 310
(b) 3100
(c) 31000
(d) 3

Answer:

(b) 3100
 In 16.534, place value of 3 = 3 hundredths = 0.03 = 3100

Page No 126:

Question 15:

Mark (✓) against the correct answer in each of the following:
478=?
(a) 4.78
(b) 4.87
(c) 4.875
(d) none of these

Answer:

(c) 4.875
478 = 4 + 78 = 4 + 0.875 = 4.875

Page No 126:

Question 16:

Mark (✓) against the correct answer in each of the following:
5.01 − 3.6 = ?
(a) 4.65
(b) 1.95
(c) 1.41
(d) none of these

Answer:

(c) 1.41
Converting into like decimals:
     5.01
 −  3.60
     1.41

Page No 126:

Question 17:

Mark (✓) against the correct answer in each of the following:
3.5 + 4.05 − 6.005 = ?
(a) 1.545
(b) 1.095
(c) 1.6
(d) none of these

Answer:

(a) 1.545

(3.50 + 4.05) - 6.005
 7.550 - 6.005
Converting into like decimals and then adding:
      3.50
   + 4.05
      7.55
Converting into like decimals and then subtracting:
     7.550
-  6.005
     1.545

Page No 126:

Question 18:

Mark (✓) against the correct answer in each of the following:
4100+710000=?
(a) 0.47
(b) 0.407
(c) 0.0407
(d) none of these

Answer:

(c) 0.0407

  4100 + 710000 = 0.04  + 0.0007
Converting into like decimals:
0.0400 + 0.0007 = 0.0407

Page No 126:

Question 19:

Mark (✓) against the correct answer in each of the following:
Among 2.6, 2.006, 2.66 and 2.08, the largest number is
(a) 2.006
(b) 2.08
(c) 2.6
(d) 2.66

Answer:

(d) 2.66
Converting all the given decimals into like decimals:
2.600, 2.006, 2.660 and 2.080
Among these given like decimals, 2.660 is the largest.

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Question 20:

Fill in the blanks.
(i) 1 m = ...... km
(ii) 10 ml = ...... 1
(iii) 16 kg 5 g = ...... kg
(iv) 2 m 8 cm = ...... m
(v) 3.02, 4.75, 1.63 are examples of ...... decimals.

Answer:

(i) 1 m = 11000 km = 0.001 km

(ii) 10 mL = 1100 1 = 0.01 L

(iii) 16 kg 5 g = (16 + 0.005) kg = 16.005 kg
(iv) 2 m 8 cm = (2 + 0.08) m = 2.08 m
(v) 3.02, 4.75, 1.63 are examples of like decimals.



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Question 21:

Write 'T' for true and 'F' for false for each of the statements given below:
(i) 3.02 < 3.2.
(ii) 3 g = 0.003 kg.
(iii) 3411000=3.410.
(iv) 6.2 and 6.200 are equivalent decimals.
(v) 2.3, 3.41, 4.53, 5.61 are examples of like decimals.

Answer:

(i) True
This is because after converting them into like decimals, we get 3.20 > 3.02, which is true.

(ii) True
1 g = 11000 kg
3 g = 31000 = 0.003 kg

(iii) False
3411000 = 0.341
This is because it is equal to 341 thousandths.

(iv) True

(v) False
In this case, every decimal should have 2 decimals in order to be like decimals. But, 2.3 has only 1 decimal.



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