Rs Aggarwal 2017 Solutions for Class 7 Math Chapter 3 Decimals are provided here with simple step-by-step explanations. These solutions for Decimals are extremely popular among Class 7 students for Math Decimals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2017 Book of Class 7 Math Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2017 Solutions. All Rs Aggarwal 2017 Solutions for class Class 7 Math are prepared by experts and are 100% accurate.

Page No 39:

Answer:

We have:

(i) 0.8=810=8÷210÷2=45

(ii) 0.75=75100 = 75÷25100÷25=34

(iii) 0.06=6100=6÷2100÷2=350

(iv) 0.285=2851000=285÷51000÷5=57200

Page No 39:

Answer:

We have:

 (i) 5.6=5610=56÷210÷2=285=535

(ii) 12.25=1225100=1225÷25100÷25=494=1214

(iii) 6.004=60041000=6004÷41000÷4=1501250=61250

(iv) 4.625=46251000=4625÷1251000÷125=378=458

Page No 39:

Answer:

(i) 4710 
    On dividing, we get:

   
   
4710 = 4.7

(ii)  156100

 On dividing, we get:

       

156100 = 1.56

(iii) 2516100

 On dividing, we get:


2516100 = 25.16

(iv) 35241000
    
  On dividing, we get:


35241000 = 3.524

(v) 258
On dividing, we get:


258 = 3.125

(vi) 325=175
  On dividing, we get:


175 = 3.4

(vii) 2225=5225
        On dividing, we get:

        

5225 = 2.08

(viii) 1720

       On dividing, we get:

      


       ∴ 1720 = 0.85

Page No 39:

Answer:

Converting the given decimals into like decimals, we have:
(i) 6.500, 16.030, 0.274 and 119.400
(ii) 3.50, 0.67, 15.60 and 4.00

Page No 39:

Answer:

We have,

(i) Comparing the whole number part, 78 > 69.
Thus, 78.23  > 69.85

(ii) Converting the decimals into like decimals, we get 3.406  and 3.460.
Comparing the whole number parts, 3 = 3
Comparing the tenths digit, 4 = 4
Comparing the hundredths digit, 6 > 0
Thus, 3.406  < 3.46

(iii)  Comparing the whole number parts, 5 = 5
Comparing the tenths digit, 6 <  8
Thus, 5.68  < 5.86

(iv) Converting the decimals into like decimals, we get 14.050 and 14.005.
Comparing the whole number parts, 14 = 14
Comparing the tenths digit, 0 = 0
Comparing the hundredths digit, 5 > 0
Thus,  14.05  > 14.005

(v) Converting the decimals into like decimals, we get 1.850 and 1.805.
Comparing the whole number parts, 1 = 1
Comparing the tenths digit, 8 = 8
Comparing the hundredths digit, 5 > 0
Thus, 1.85 > 1.805

(vi)  Comparing the whole number parts, 0 < 1
Thus, 0.98 < 1.07

Page No 39:

Answer:

(i) Converting the given decimals into like decimals, we get:
     4.60, 7.40, 4.58, 7.32, 4.06
     Clearly, 4.06 < 4.58 < 4.60 < 7.32 < 7.40
     Hence, the given decimals in ascending order are 4.06, 4.58, 4.6, 7.32 and 7.4.

(ii) Converting the given decimals into like decimals, we get:
      0.50, 5.50, 5.05, 0.05, 5.55
      Clearly, 0.05 < 0.50 < 5.05< 5.50 < 5.55
      Hence, the given decimals in ascending order are 0.05, 0.5, 5.05, 5.5 and 5.55.

(iii) Converting the given decimals into like decimals, we get:
        6.84, 6.48, 6.80, 6.40, 6.08
        Clearly, 6.08 < 6.40 < 6.48 < 6.80< 6.84
        Hence, the given decimals in ascending order are 6.08, 6.4, 6.48, 6.8 and 6.84.

(iv)  Converting the given decimals into like decimals, we get:
        2.200, 2.202, 2.020, 22.200, 2.002
        Clearly, 2.002 < 2.020 < 2.200 < 2.202 < 22.200
        Hence, the given decimals in ascending order are 2.002, 2.02, 2.2, 2.202 and 22.2.

Page No 39:

Answer:

(i) Converting the given decimals into like decimals, we get:
     7.40, 8.34, 74.40, 7.44, 0.74
     Clearly, 74.40 > 8.34 > 7.44 > 7.40 > 0.74
     Hence, the given decimals in descending order are 74.4, 8.34, 7.44, 7.4 and 0.74.

(ii) Converting the given decimals into like decimals, we get:
      2.600, 2.260, 2.060, 2.007, 2.300
      Clearly, 2.600 > 2.300 > 2.260 > 2.060 > 2.007
      Hence, the given decimals in descending order are 2.6, 2.3, 2.26, 2.06 and 2.007.

Page No 39:

Answer:

45 mm = 4510 cm = 4.5 cm

            = 4.5 cm = 4.5100 m = 0.045 m

            = 0.045 m = 0.0451000 km = 0.000045 km

∴ 45 mm = 4.5 cm = 0.045 m = 0.000045 km

Page No 39:

Answer:

We have:
(i) 8 paise = Rs 8100 = Rs 0.08

(ii) 9 rupees 75 paise = Rs 9+75100 = Rs (9 + 0.75) = Rs 9.75

(iii) 8 rupees 5 paise  = Rs 8+ 5100 = Rs (8 + 0.05) = Rs 8.05

Page No 39:

Answer:

We have:

(i) 65 m = 651000 km = 0.065 km
     ∴ 65 m = 0.065 km

(ii) 284 m = 2841000km = 0.284 km

(iii) 3 km 5 m = 3+ 51000 = 3+ 0.005 = 3.005 km
                                                     



Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
16.00, 8.70, 0.94, 6.80 and 7.77
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 40.21

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
18.600, 206.370, 8.008, 26.400 and 6.900
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 266.278.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
63.50, 9.70, 0.80, 26.66 and 12.17
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 112.83.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
17.400, 86.390, 9.435, 8.800 and 0.060
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 122.085.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
26.900, 19.740, 231.769 and 0.048
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 278.457.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
23.800, 8.940, 0.078 and 214.600
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 247.418.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
6.606, 66.600, 666.000, 0.066 and 0.660
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 739.932.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
9.090, 0.909, 99.900, 9.990 and 0.099
Writing these decimals in column form and adding, we get:

Hence, the sum of the given decimals is 119.988.

Page No 41:

Answer:

The given decimals are like decimals. Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (72.43 − 14.79) = 57.64

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
36.74 and 52.60
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (52.60 − 36.74) = 15.86

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
13.876 and 22.000
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (22.000 − 13.876) = 8.124

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
15.079 and 24.160
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (24.160 − 15.079) = 9.081

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
0.680 and 1.007
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (1.007 − 0.680) = 0.327

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
0.4678 and 5.0500
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (5.0500 − 0.4678) = 4.5822

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
2.5307 and 8.0000
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (8.0000 − 2.5307) = 5.4693

Page No 41:

Answer:

Writing the given like decimals in column form with the larger one at the top and subtracting them, we get:

∴ (9.001 − 6.732) = 2.269

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
5.746 and 9.100
Writing them in column form with the larger one at the top and subtracting them, we get:

∴ (9.100 − 5.746) = 3.354

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
63.58 and 92.00
Thus, required number = (92.00 − 63.58) = 28.42
Hence, 28.42 should be added to 63.58 to get 92.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
8.100 and 0.813
Thus, required number = (8.100 − 0.813) = 7.287
Hence, 7.287 should be subtracted from 8.1 to get 0.813.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
32.67 and 60.10
Thus, required number = (60.10 − 32.67) = 27.43
Hence, 32.67 should be increased by 27.43 to get 60.1.

Page No 41:

Answer:

Converting the given decimals into like decimals, we get:
74.30 and 26.87
Thus, required number = (74.30 − 26.87) = 47.43
Hence, 74.3 should be decreased by 47.43 to get 26.87.

Page No 41:

Answer:

Total amount spent by Rohit on purchasing of the given articles = Rs (23.75 + 2.85 + 15.90)
                                                                                                 = Rs 42.50
Money given to the shopkeeper = Rs 50
∴ Money returned by the shopkeeper = Rs (50 − 42.50)
                                                          = Rs 7.50
Thus, amount received by Rohit = Rs 7.50



Page No 43:

Answer:

We have the following:

(i) 73.92 × 10 = 739.2                 [Shifting the decimal point to the right by 1 place]
(ii) 7.54 × 10 = 75.4                    [Shifting the decimal point to the right by 1 place]
(iii) 84.003 × 10 = 840.03           [Shifting the decimal point to the right by 1 place]
(iv) 0.83 × 10 = 8.3                     [Shifting the decimal point to the right by 1 place]
(v) 0.7 × 10 = 7                           [Shifting the decimal point to the right by 1 place]
(vi) 0.032 × 10 = 0.32                 [Shifting the decimal point to the right by 1 place]



Page No 44:

Answer:

We have the following:

(i) 2.397 × 100 = 239.7           [Shifting the decimal point to the right by 2 places]
(ii) 6.83 × 100 = 683               [Shifting the decimal point to the right by 2 places]
(iii) 2.9 × 100 = 290                [Shifting the decimal point to the right by 2 places]
(iv) 0.08 ×100 = 8                   [Shifting the decimal point to the right by 2 places]
(v) 0.6 × 100 = 60                   [Shifting the decimal point to the right by 2 places]
(vi) 0.003 × 100 = 0.3             [Shifting the decimal point to the right by 2 places]

Page No 44:

Answer:

We have:
(i) 6.7314 × 1000 = 6731.4            [Shifting the decimal point to the right by 3 places]
(ii) 0.182 × 1000 = 182                  [Shifting the decimal point to the right by 3 places]          
(iii) 0.076 × 1000 = 76                   [Shifting the decimal point to the right by 3 places]
(iv) 6.25 × 1000 = 6250                  [Shifting decimal point to the right by 3 places]
(v) 4.8 × 1000 = 4800                     [Shifting the decimal point to the right by 3 places]
(vi) 0.06 × 1000 = 60                      [Shifting the decimal point to the right by 3 places]

Page No 44:

Answer:

We have the following:

(i)      54 × 16 = 864
     ∴ 5.4 × 16 = 86.4                            [1 place of decimal]

(ii)    365 × 19 = 6935
       ∴ 3.65 × 19 = 69.35                      [2 places of decimal]

(iii)  854 × 12 = 10248
        ∴ 0.854 × 12 = 10.248                 [3 places of decimal]

(iv)  3673 × 48 = 176304
       ∴ 36.78 × 48 = 1763.04                [2 places of decimal]

(v) 4125 × 86 = 354750
      ∴ 4.125 × 86 = 354.750                [3 places of decimal] 
                           = 354.75

(vi) 10406 × 75 = 780450
      ∴ 104.06 × 75 = 7804.50               [2 places of decimal]       
                              = 7804.5

(vii)  6032 × 124 = 747968
        ∴ 6.032 × 124 = 747.968             [3 places of decimal] 

(viii) 146 × 69 = 10074          
         ∴ 0.0146 × 69 = 1.0074              [4 places of decimal] 

(ix) 125 × 327 = 40875
       ∴ 0.00125 × 327 = 0.40875           [5 places of decimal]   

Page No 44:

Answer:

(i) First, we will multiply 76 by 24.
    
∴ 76 × 24 = 1824
Sum of decimal places in the given numbers = (1 + 1) = 2
∴ 7.6 × 2.4 = 18.24     [2 places of decimal]

(ii) First, we will multiply 345 by 63.
    
∴ 345 × 63 = 21735
Sum of decimal places in the given numbers = (2 + 1) = 3
∴ 3.45 × 6.3 = 21.735     [3 places of decimal]

(iii) First, we will multiply 54 by 27.
      
∴ 54 × 27 = 1458
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.54 × 0.27 = 0.1458    [4 places of decimal]

(iv) First, we will multiply 568 by 49.
      
∴ 568 × 49 = 27832
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.568 × 4.9 = 2.7832    [4 places of decimal]

(v) First, we multiply 654 by 9.
     
∴ 654 × 9 = 5886
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 6.54 × 0.09 = 0.5886     [4 places of decimal]

(vi) First, we will multiply 387 by 125.
      
∴ 387 × 125 = 48375
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 3.87 × 1.25 = 4.8375    [4 places of decimal]

(vii) First, we will multiply 38 by 6.
        
∴ 38 × 6 = 228
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.06 × 0.38 = 0.0228    [4 places of decimal]

(viii) First, we will multiply 623 by 75.
        
∴ 623 × 75 = 46725
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.623 × 0.75 = 0.46725    [5 places of decimal]

(ix) First, we will multiply 14 by 46.
      
∴ 14 × 46 = 644
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.014 × 0.46 = 0.00644    [5 places of decimal]

(x) First, we will multiply 545 by 176.
     
∴ 545 × 176 = 95920
Sum of decimal places in the given numbers = (1 + 2) = 3
∴ 54.5 × 1.76 = 95.920  [3 places of decimal]
                       = 95.92

(xi) First, we will multiply 45 by 24.
      
∴ 45 × 24 = 1080
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.045 × 2.4 = 0.1080    [4 places of decimal]
                       = 0.108

(xii) First, we will multiply 1245 by 64.
       
∴ 1245 × 64 = 79680
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 1.245 × 6.4 = 7.9680   [4 places of decimal]
                       = 7.968

Page No 44:

Answer:

(i) First, we will find the product 13 ⨯ 1.3 ⨯ 0.13.
     Now, 13 ⨯ 13 ⨯ 13 = 169 x 13
                                    = 2197
    
     Sum of decimal places in the given numbers = (1 + 2) = 3
     So, the product must have three decimal places.

     ∴ 13 ⨯ 1.3 ⨯ 0.13 = 2.197

(ii) First, we will find the product 2.4 ⨯ 1.5 ⨯ 2.5.
     Now, 24 ⨯ 15 ⨯ 25 = 360 x 25
                                   = 9000
    
     Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
     So, the product must have three decimal places.

     ∴ 2.4 ⨯ 1.5 ⨯ 2.5 = 9.000
                                 = 9

(iii) First, we will find the product 0.8 ⨯ 3.5 ⨯ 0.05.
       Now, 8 ⨯ 35 ⨯ 5 = 280 ⨯ 5
                                 = 1400
      
       Sum of decimal places in the given numbers = (1 + 1 + 2) = 4
       So, the product must have four decimal places.

       ∴ 0.8 ⨯ 3.5 ⨯ 0.05 = 0.1400
                                     = 0.14

(iv) First, we will find the product 0.2 ⨯ 0.02 ⨯ 0.002.
       Now, 2 ⨯ 2 ⨯ 2 = 4 ⨯ 2
                                = 8
       Sum of decimal places in the given numbers = (1 + 2 + 3) = 6
       So, the product must have six decimal places.
      
∴ 0.2 ⨯ 0.02 ⨯ 0.002 = 0.000008

(v) First, we will find the product 11.1 ⨯ 1.1 ⨯ 0.11.
       Now, 111 ⨯ 11 ⨯ 11 = 1221 ⨯ 11
                                       = 13431
      
       Sum of decimal places in the given numbers = (1 + 1 + 2) = 4
       So, the product must have four decimal places.

       ∴ 11.1 ⨯ 1.1 ⨯ 0.11 = 1.3431

(vi) First, we will find the product 2.1 ⨯ 0.21 ⨯ 0.021.
       Now, 21 ⨯ 21 ⨯ 21 = 441 ⨯ 21
                                     = 9261
      
       Sum of decimal places in the given numbers = ( 1 + 2 + 3) = 6
       So, the product must have six decimal places.

       ∴ 2.1 ⨯ 0.21 ⨯ 0.021 = 0.009261

Page No 44:

Answer:

(i) (1.2)2 = 1.2 × 1.2
     First, we will find the product 1.2 × 1.2.
     Now, 12 × 12 = 144
     Sum of decimal places in the given numbers = (1 + 1) = 2
     So, the product must have two decimal places.

     ∴ (1.2)2 = 1.2× 1.2 = 1.44

(ii) (0.7)2 = 0.7 × 0.7
      First, we will find the product 0.7 × 0.7.
      Now, 7 × 7 = 49
      Sum of decimal places in the given numbers = (1 + 1) = 2
      So, the product must have two decimal places.
      ∴ (0.7)2 = 0.7 × 0.7 = 0.49

(iii) (0.04)2 = 0.04 × 0.04
       First, we will find the product 0.04 × 0.04.
       Now, 4× 4 = 16
       Sum of decimal places in the given numbers = (2 + 2) = 4
       So, the product must have four decimal places.
       ∴ (0.04)2 = 0.04× 0.04 = 0.0016

(iv) (0.11)2 = 0.11 × 0.11
       First, we will find the product 0.11 × 0.11.
       Now, 11 × 11 = 121
       Sum of decimal places in the given numbers = ( 2 + 2) = 4
       So, the product must have four decimal places.
       ∴ (0.11)2 = 0.11 × 0.11 = 0.0121

Page No 44:

Answer:

(i) (0.3)3 = 0.3 × 0.3 × 0.3
     First, we will find the product 3 × 3 × 3.
     Now, 3 × 3 × 3 = 27
     Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
     So, the product must have three places of decimal.
     ∴ (0.3)3 = 0.3 × 0.3 × 0.3 = 0.027

(ii) (0.05)3 = 0.05 × 0.05 × 0.05
     First, we will find the product 5 × 5 × 5.
     Now, 5 ×5 × 5 = 125
     Sum of decimal places in the given numbers = (2 + 2 + 2) = 6
     So, the product must have six decimal places.
     ∴ (0.05)3 = 0.05 × 0.05 × 0.05 = 0.000125

(iii) (1.5)3 = 1.5 ×1.5 ×1.5
       First, we will find the product 15 ×15 × 15.
       Now, 15 ×15 × 15 = 225 × 15 = 3375
      
       Sum of decimal places in the given numbers = (1 + 1 + 1) = 3
       So, the product must have three decimal places.
       ∴ (1.5)3 = 1.5 × 1.5 × 1.5 = 3.375

Page No 44:

Answer:

Distance covered by the bus in 1 hour = 62.5 km
∴ Distance covered in 18 hours = (62.5 × 18) km
                                                            = 1125 km
Hence, the bus can cover a distance of 1125 km in 18 hours.

Page No 44:

Answer:

Weight of 1 tin of oil = 16.8 kg
∴ Weight of 45 such tins = (16.8 × 45) kg
                                              = 756 kg
Hence, the weight of 45 tins of oil is 756 kg.

Page No 44:

Answer:

Weight of 1 bag of wheat = 97.8 kg
∴ Weight of 500 such bags = (97.8 x 500) kg
                                               = 48900 kg
Hence, the weight of 500 bags of wheat is 48900 kg.

Page No 44:

Answer:

Weight of 1 bag of sugar = 48.450 kg
∴ Weight of 16 bags of sugar = (48.450 ⨯ 16) kg
                                                     = 775.2 kg


Hence, the weight of 16 bags of sugar is 775.2 kg.

Page No 44:

Answer:

Capacity of 1 sauce bottle = 0.845 kg
∴ Capacity of 72 such bottles = (0.845 × 72) kg
                                                     = 60.84 kg

Hence, the capacity of 72 bottles of sauce will be 60.84 kg.

Page No 44:

Answer:

Weight of 1 bottle of jam = 925 g =0.925 kg
∴ Weight of 25 such bottles = (0.925 × 25) kg
                                                   = 23.125 kg

∴ The weight of 25 bottles of jam will be 23.125 kg.

Page No 44:

Answer:

Capacity of 1 drum of oil = 16.850 litres
∴ Capacity of 48 such drums = (16.850 x 48) litres
                                                     = 808.800 litres

Hence, the capacity of 48 drums of oil is 808.800 litres.

Page No 44:

Answer:

Cost of 1 kg of rice =Rs 56.80
∴ Cost of 16.25 kg of rice = Rs (56.80 × 16.25)
                                                = Rs 923

Hence, the cost of 16.25 kg of rice is Rs 923.

Page No 44:

Answer:

Cost of 1 m of cloth = Rs 108.50
∴ Cost of 18.5 m of cloth = Rs (108.50 x 18.5)
                                              = Rs 2007.25

Hence, the cost of 18.5 m of cloth is Rs 2007.25.

Page No 44:

Answer:

Distance covered by the car with 1 litre of petrol = 8.6 km
∴ Distance covered with 36.5 litres of petrol = (8.6 × 36.5) km
                                                                                   = 313.900 km
Hence, the distance covered by the car with 36.5 litres of petrol is 313.900 km.

Page No 44:

Answer:

Charges for 1 km = Rs 9.80
∴ Charges for 106.5 km = Rs (9.80 × 106.5)
                                             = Rs 1043.70
Hence, the taxi driver will charge Rs 1043.70 for a journey of 106.5 km.



Page No 49:

Answer:

We have the following:

(i) 131.6 ÷ 10 = 131.610=13.16                      [Shift the decimal point to the left by 1 place]

(ii) 32.56 ÷ 10 = 32.5610=3.256                    [Shift the decimal point to the left by 1 place]

(iii) 4.38 ÷ 10 = 4.3810=0.438                       [Shift the decimal point to the left by 1 place]

(iv) 0.34 ÷ 10 = 0.3410=0.034                       [Shift the decimal point to the left by 1 place]

(v) 0.08 ÷ 10 = 0.0810=0.008                        [Shift the decimal point to the left by 1 place]

(vi) 0.062 ÷ 10 = 0.06210=0.0062                 [Shift the decimal point to the left by 1 place]

Page No 49:

Answer:

We have the following:

(i) 137.2 ÷ 100 = 137.2100=1.372                          [Shifting the decimal point to the left by 2 places]

(ii) 23.4 ÷ 100 =23.4100=0.234                              [Shifting the decimal point to the left by 2 places]

(iii) 4.7 ÷ 100 = 4.7100=0.047                               [Shifting the decimal point to the left by 2 places]

(iv) 0.3 ÷ 100 = 0.3100=0.003                               [Shifting the decimal point to the left by 2 places]

(v) 0.58 ÷ 100 = 0.58100=0.0058                           [Shifting the decimal point to the left by 2 places]

(vi) 0.02 ÷ 100 = 0.02100=0.0002                          [Shifting the decimal point to the left by 2 places]

Page No 49:

Answer:

We have the following:

(i) 1286.5 ÷ 1000 = 1286.51000=1.2865                 [Shift the decimal point to the left by 3 places]

(ii) 354.16 ÷ 1000 = 354.161000=0.35416              [Shift the decimal point to the left by 3 places]

(iii) 38.9 ÷ 1000 = 38.91000=0.0389                      [Shift the decimal point to the left by 3 places]

(iv) 4.6 ÷ 1000 = 4.61000=0.0046                        [Shift the decimal point to the left by 3 places]

(v) 0.8 ÷ 1000 = 0.81000=0.0008                         [Shift the decimal point to the left by 3 places]

(vi) 2 ÷ 1000 = 21000=0.002                           [Shift the decimal point to the left by 3 places]

Page No 49:

Answer:

(i) 12 ÷ 8 = 128=32
     

  ∴ 12 ÷ 8 = 1.5

(ii) 63 ÷ 15 = 6315=215
     
   ∴ 63 ÷ 15 = 4.2

(iii) 47 ÷ 20 = 4720
      
        ∴ 47 ÷ 20 = 2.35

(iv) 101 ÷ 25 = 10125
      
       ∴ 101 ÷ 25 = 4.04

(v ) 31 ÷ 40
    
    
    ∴ 31 ÷ 40 = 0.775

(vi) 11 ÷ 16 = 1116
      
      
       ∴ 11 ÷ 16 = 0.6875    

Page No 49:

Answer:

(i) We have:
      43.2 ÷ 6
      
       ∴ 43.2 ÷ 6 = 7.2
(ii) We have:
       60.48 ÷ 12
       
        ∴ 60.48 ÷ 12 = 5.04

(iii) We have:
        117.6 ÷ 21
       
      ∴ 117.6 ÷ 21 = 5.6

(iv) We have:
        217.44 ÷ 18
       
     ∴ 217.44 ÷ 18 = 12.08

(v) We have:
      2.575 ÷ 25
     
       ∴ 2.575 ÷ 25 = 0.103

(vi) We have:
       6.08 ÷ 8
      
      ∴ 6.08 ÷ 8 = 0.76

(vii) We have:
        0.765 ÷ 9
       
       ∴ 0.765 ÷ 9 = 0.085

(viii) We have:
          0.768 ÷ 16
         
      ∴ 0.768 ÷ 16 = 0.048
(ix) We have:
        0.175 ÷ 25

=0.17525=0.175×100025×1000=17525×1000=71000=0.007

(x) We have:
      0.3322 ÷ 11
     
     ∴ 0.3322 ÷ 11 = 0.0302

(xi) We have:
       2.13 ÷ 15
      
     ∴ 2.13 ÷ 15 = 0.142

(xii) We have:
         6.54 ÷ 12
        
      ∴ 6.54 ÷ 12 = 0.545

(xiii) We have:
         5.52 ÷ 16
        
     ∴ 5.52 ÷ 16 = 0.345

(xiv) We have:
         1.001 ÷ 14
         
    ∴ 1.001 ÷ 14 = 0.0715

(xv) We have:
       0.477 ÷ 18
       
        ∴ 0.477 ÷ 18 =  0.0265

Page No 49:

Answer:

(i) 16.46 ÷ 20 = 16.4620=16.46×10020×100=16462×1000=8231000=0.823

(ii) 403.8 ÷ 30 = 403.830=403.8×1030×10=40383×100=1346100=13.46

(iii) 19.2 ÷ 80 = 19.280=19.2×1080×10=192800=1928×100=24100=0.24

(iv) 156.8 ÷ 200 = 156.8200=156.8×10200×10=15682000=7841000=0.784

(v) 12.8 ÷ 500 = 12.8500=12.8×10500×10=1285000=25.61000=0.0256

(vi) 18.08 ÷ 400 = 18.08400=18.08×100400×100=180840000=45210000=0.0452

Page No 49:

Answer:

(i) 3.28 ÷ 0.8 = 3.280.8=3.28×100.8×10=32.88
Now, we have:

     
       ∴ 3.280.8=32.88=4.1

(ii)  0.288 ÷ 0.9 = 0.2880.9=0.288×100.9×10=2.889
Now, we have:

      
      ∴ 0.2880.9=2.889=0.32

(iii)  25.395 ÷ 1.5 = 25.3951.5=25.395×101.5×10=253.9515
Now, we have:

        
       ∴ 25.3951.5=253.9515=16.93

(iv) 2.0484 ÷ 0.18 = 2.04840.18=2.0484×1000.18×100=204.8418
Now, we have:

       
     ∴ 2.04840.18=204.8418=11.38

(v)  0.228 ÷ 0.38 = 0.2280.38=0.228×1000.38×100=22.838
Now, we have:
      

     ∴ 0.2280.38=22.838=0.6

(vi) 0.8085 ÷ 0.35 = 0.80850.35=0.8085×1000.35×100=80.8535
Now, we have:

      
      ∴0.80850.35=80.8535=2.31

(vii) 21.976 ÷ 1.64 = 21.9761.64=21.976×1001.64×100=2197.6164
Now, we have:

       
        ∴ 21.9761.64=2197.6164=13.4

(viii) 11.04 ÷ 1.6 = 11.041.6=11.04×101.6×10=110.416
Now, we have:
          

       ∴11.041.6=110.416=6.9
     
(ix)  6.612 ÷ 11.6 = 6.61211.6=6.612×1011.6×10=66.12116
Now, we have:
      
       ∴ 6.61211.6=66.12116=0.57

(x) 0.076 ÷  0.19 = 0.0760.19=0.076×1000.19×100=7.619
Now, we have:
    
    ∴ 0.0760.19=7.619=0.4

(xi) 48 ÷ 0.074
 
=1480.074=148×10000.074×1000=14800074=2×1000=2000

(xii)  16.578 ÷ 5.4 = 16.5785.4=16.578×105.4×10=165.7854
Now, we have:

        
        ∴ 16.5785.4=165.7854=3.07

(xiii)  28 ÷ 0.56

=280.56=28×1000.56×100=280056=1×1002=50


(xiv) 204 ÷ 0.17

=2040.17=204×1000.17×100=2040017=12×100=1200

(xv) 3 ÷ 80 = 380

Now, we have:

      
       ∴ 380 = 0.0375



Page No 50:

Answer:

Cost of 24 chairs = Rs 9255.60
∴ Cost of one chair = Rs 9255.6024
                                     = Rs 9255.60×1024×10
                                       = Rs 92556240
                                       = Rs 385.65


Hence, the cost of one chair is Rs 385.65.

Page No 50:

Answer:

Cloth required for 1 shirt = 1.8 m
∴ Number of shirts that can be made from 45 m of cloth =  451.8 = 150.6 =50.2 = 502= 25

Hence, 25 shirts can be made from a piece of cloth of length 45 m.

Page No 50:

Answer:

Distance covered by the car with 2.4 litres of petrol = 22.8 km
∴ Distance covered with 1 litre of petrol = 22.82.4 km
                                                                         = 22824 km = 228÷1224÷12 km = 192 km = 912 km

Hence, the distance covered by the car with 1 litre of petrol is 912 km.
                                                          

Page No 50:

Answer:

Capacity of 1 tin of oil = 16.5 litres
∴ Number of tins required to hold 478.5 litres of oil = 478.516.5=4785165=4785÷15165÷15=31911=29
Hence, 29 oil tins will be required to hold 478.5 litres of oil.

Page No 50:

Answer:

Weight of 37 bags of sugar = 3644.5 kg
∴ Weight of 1 bag of sugar = 3644.537 = 98.5 kg

Hence, each bag of sugar weighs 98.5 kg.

Page No 50:

Answer:

Capacity of 69 buckets of water = 586.5 litres
∴ Capacity of one such bucket = 586.569 litres = 8.5 litres.
    
Hence, the capacity of each water bucket is 8.5 litres.

Page No 50:

Answer:

Length of one piece of cloth = 1.15 m
∴ Number of pieces she gets from 46 m of cloth = 461.15
                                                                                        = 46×1001.15×1004600115 = 40

Hence, Monica has 40 pieces of cloth each of length 1.15 m.

Page No 50:

Answer:

Total weight of all the bags of cement = 1792.8 kg
Weight of each bag = 49.8 kg
Number of bags = Total weightWeight of each bag
                           = 1792.849.8=17928498=36
                       
Hence, Mr. Soni bought 36 bags of cement.

Page No 50:

Answer:

Thickness of the pile of plywood pieces = 1.89 m = 189 cm
Thickness of one piece of plywood = 0.35 cm
∴ Required number of plywood pieces = 1890.35=189×1000.35×100=1890035=540
   
Hence, 540 pieces of plywood are required to make a pile of height 1.89 m.

Page No 50:

Answer:

Product of the given decimals = 261.36
 One decimal = 17.6
The other decimal = 261.36 ÷ 17.6
                              = 261.3617.6=261.36×1017.6×10=2613.6176
                                 = 14.85

Hence, the other decimal is 14.85.

Page No 50:

Answer:

(b) 350

0.06 = 6100=350

Page No 50:

Answer:

(c) 1125

1.04 = 104100=2625=1125

Page No 50:

Answer:

(b) 2.08

2225=5225
 
On dividing, we get:

        

2225=5225 = 2.08

Page No 50:

Answer:

(c) 0.00006 km

6 cm = 6100m = 0.06 m

0.06 m = 0.061000 km = 0.00006 km

∴ 6 cm = 0.00006 km

Page No 50:

Answer:

(b) 0.07 kg

70 g =701000 kg = 7100 kg

         = 0.07 kg

∴ 70 g = 0.07 kg

Page No 50:

Answer:

(c) 5.006 kg

5 kg 6 g = (5 × 1000) g + 6 g = 5006 g

= 50061000 kg = 5.006 kg

∴ 5 kg 6 g = 5.006 kg

Page No 50:

Answer:

(c) 2.005 km

2 km 5 m = (2 × 1000) m + 5 m = 2005 m

20051000 km = 2.005 km

∴ 2 km 5 m = 2.005 km

Page No 50:

Answer:

(c) 0.307

Converting the given decimals into like decimals, we get:
1.007 and 0.700
Writing them in column form with the larger one at the top and subtracting, we get:

Hence, the required number is 0.307.

Page No 50:

Answer:

(b) .07

We have:
0.1 − x = 0.03
⇒ x = 0.1 − 0.03

Converting the given decimals into like decimals, we get:
0.10 and 0.03

Writing them in column form with the larger one at the top and subtracting, we get:

∴ x = 0.07
Hence, the required number is 0.07.



Page No 51:

Answer:

(c) .43
We have:
3.07 + x = 3.5
 x = 3.5 − 3.07
Converting the given decimals into like decimals, we get:
3.07 and 3.50
Writing them in column form with the larger one at the top and subtracting, we get:

∴ x  = 0.43

Hence, 0.43 should be added to 3.07 to get 3.5.

Page No 51:

Answer:

(c) 0.069
First, we will multiply 23 by 3.
i.e., 23 × 3 = 69
Sum of decimal places in the given decimals  = (2 + 1) = 3
∴ 0.23 × 0.3 = 0.069     ( 3 places of decimal)

Page No 51:

Answer:

(b) 0.6
We have:
2 × 30 = 60
∴ 0.02 × 30 = 0.60            (2 places of decimal)
                        = 0.6

Page No 51:

Answer:

(b) 0.2
First, we will multiply 25 by 8.
∴ 25 × 8 = 200
Sum of decimal places in the given decimals = (2 + 1) = 3
∴ 0.25 × 0.8 = 0.200    [3 places of decimal]
                        = 0.2

Page No 51:

Answer:

(c) .064

First, we will find the product 4 × 4 × 4 = 64
Sum of decimal places in the given decimals = (1 + 1 + 1) = 3
∴ 0.4 × 0.4 × 0.4 = 0.064   ( 3 places of decimal)

Page No 51:

Answer:

(b) .0011

First, we will find the product 11 × 1 × 1.
Sum of decimal places in the given decimals  = (1 + 1 + 2) = 4
∴ 1.1 ×  0.1 × 0.01 = 0.0011   (4 places of decimal)

Page No 51:

Answer:

(a) 13

2.08 ÷ 0.16 = 2.080.16 = 2.08×1000.16×100 = 20816=13

Page No 51:

Answer:

(b) 0.17

1.02 ÷ 6 = 1.026=1.02×1006×100=1026×100=17100=0.17

Page No 51:

Answer:

(a) 44.2

30.94 ÷ 0.7 = 30.940.7=30.94×1000.7×100=309470=44.2

Page No 51:

Answer:

(b) 2.1

2.73 ÷ 1.3 = 2.731.3= 2.73×1001.3×100 = 27313×10 = 2110 = 2.1

Page No 51:

Answer:

(a) 40.5

89.1 ÷ 2.2 = 89.12.2 = 89.1 × 102.2 × 10 = 89122 = 40.5

Page No 51:

Answer:

(c) 0.025
First, we will multiply 5 by 5.
i.e., 5 × 5 = 25
Sum of decimal places in the given decimals = (1 + 2) = 3
∴ 0.5 × 0.05 = 0.025   (3 places of decimal)



Page No 53:

Answer:

Cost of 1 pen = Rs 32.50
∴ Cost of 24 such pens = Rs (32.50 × 24)
                                      = Rs 780
Hence, the cost of 24 pens is Rs 780.

Page No 53:

Answer:

Distance covered by the bus in 1 h = 64.5 km
∴ Distance covered in 18 h = (64.5 × 18) km
                                             = 1161 km

Hence, the bus can cover a distance of 1161 km in 18 h.

Page No 53:

Answer:

First, we will find the product 68 × 65 × 4.
Now, 68 × 65 × 4 = 4420 × 4 = 17680
Sum of decimal places in the given decimals = (2 + 1 + 2) = 5
So, the product have five decimal places.

∴ 0.68 × 6.5 × 0.04 = 0.17680
                                   = 0.1768

Page No 53:

Answer:

Total weight of all the bags = 2231 kg
Weight of each bag = 48.5 kg

Number of bags = Total weightWeight of each bag

                           =223148.5kg

                           = 2231×1048.5×10=22310485= 46

Hence, 46 bags of cement will weigh 2231 kg.

Page No 53:

Answer:

(i) 0.196 ÷ 1.4 =0.1961.4=0.196×101.4×10=1.9614=0.14

    

(ii) 39.168 ÷ 1.2 =39.1681.2=39.168×101.2×10=391.6812=32.64

      

(iii) 0.228 ÷ 0.38 = 0.2280.38=0.228×1000.38×100=22.838=0.6

      

Page No 53:

Answer:

Product of the given decimals = 1.824
One decimal = 0.64
The other decimal = 1.824 ÷ 0.64
                              = 1.8240.64=1.824×1000.64×100=182.464=2.85

Hence, the other decimal is 2.85.

Page No 53:

Answer:

Thickness of the pile of plywoods = 2.43 m = 2.43 × 100 cm = 243 cm
Thickness of one piece of plywood = 0.45 cm
∴ Required number of pieces of plywood = 2430.45=243×1000.45×100=2430045=540
   
   
Hence, the required number of pieces of plywood is 540.

Page No 53:

Answer:

Let the number of sides of the polygon be n.
Length of each side of the polygon = 3.8 cm
∴ Perimeter of the polygon = (3.8 × n) cm
But it is given that its perimeter is 22.8 cm.
∴ (3.8 × n) cm = 22.8 cm
n = 22.83.8 = 22838 = 6

Hence, the given polygon has six sides.

Page No 53:

Answer:

(b) 2.04

2125=5125 = 2.04

Page No 53:

Answer:

(b) 11125

1.008 = 1.008 × 10001 × 1000=10081000=1008 ÷ 41000 ÷ 4=126125=11125

Page No 53:

Answer:

(c) 2.005 kg

2 kg 5 g = (2 × 1000) g + 5 g = (2005) g

              = 20051000 kg = 2.005 kg

Page No 53:

Answer:

(b) 0.08

We have:
0.012 ÷ 0.15 = 0.0120.15=0.012×1000.15×100=1.215=0.08

Page No 53:

Answer:

(c) .0011
First, we will find the product 11 × 1 × 1.
i.e., 11 × 1 × 1 = 11 × 1 = 11
Sum of decimal places in the given decimals = (1 + 1 + 2) = 4

∴ 1.1 ×  0.1 × 0.01 = 0.0011   [4 places of decimal]

Page No 53:

Answer:

(b) 2.03

4.669 ÷ 2.3  = 4.6692.3=4.669×102.3×10=46.6923=2.03

Page No 53:

Answer:

Option (c) is correct.
Let the number added be x.
We have:
2.06 + x = 3.1
x = 3.1 − 2.06

Converting the given decimals into like decimals, we get:
2.06 and 3.10
Thus, required number = (3.10 − 2.06) = 1.04

Hence, 1.04 should be added to 2.06 to get 3.1.

Page No 53:

Answer:

(b) 0.06
We have:
0.1 − x  = 0.04
x = 0.1 − 0.04
Converting the given decimals into like decimals, we get:
0.10 and 0.04
Thus, required number = (0.10 − 0.04) = 0.06
Hence, 0.06 should be subtracted from 0.1 to get 0.04.

Page No 53:

Answer:

(i) 1.001 ÷ 14 = 0.0715

     Explanation: 1.00114=0.0715
     

(ii) 204 ÷ 0.17 = 1200

      Explanation: 2040.17=204×1000.17×100=204×10017=12×100=1200

(iii) 0.47 × 5.3 = 2.491

       Explanation: First, we will multiply 47 by 53.
                              
        ∴ 47 × 53 = 2491
        Sum of decimal places in the given decimals = (2 + 1) = 3
        ∴ 0.47 × 5.3 = 2.491

(iv) (0.7)2 = 0.49
        Explanation: (0.7)2 = 0.7 × 0.7
        First, we will find the product 0.7 × 0.7.
        Now, 7 × 7 = 49
        Sum of decimal places in the given decimals = (1 + 1) = 2
        So, the product must have two decimal places.
        ∴ (0.7)2 = 0.7 × 0.7 = 0.49

(v) (0.05)3 = 0.000125
      Explanation:  First, we will find the product 0.05 × 0.05 × 0.05.
      Now, 5 × 5 × 5 = 125
      Sum of decimal places in the given decimals = (2 + 2 + 2) = 6
      So, the product must have six decimal places.
      ∴ (0.05)3 = 0.05 × 0.05 × 0.05 = 0.000125
     

Page No 53:

Answer:

(i) T
We have:
0.5 × 0.05
Now, 5 × 5 = 25
Sum of decimal places in the given decimals = ( 1 + 2) = 3
∴ 0.5 × 0.05 = 0.025

(ii) T
We have:
0.25 × 0.8
Now, 25 × 8 = 200
Sum of decimal places in the given decimals = (2 +1) = 3
∴ 0.25 × 0.8 =0.200 = 0.2


(iii) T
We have:
0.35 ÷ 0.7 = 0.350.7=0.35×100.7×10=3.57=0.5

(iv) F
We have:
0.4 × 0.4 × 0.4
Now, 4 × 4 × 4 = 64
Sum of decimal places in the given decimals = (1 +1 +1) = 3
 ∴ 0.4 × 0.4 × 0.4 = 0.064

(v) T
6 cm = 6100 m = 0.06 m



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