Rs Aggarwal 2020 2021 for Class 7 Maths Chapter 3 - Decimals

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Rs Aggarwal 2020 2021 Solutions for Class 7 Maths Chapter 3 Decimals are provided here with simple step-by-step explanations. These solutions for Decimals are extremely popular among Class 7 students for Maths Decimals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2020 2021 Book of Class 7 Maths Chapter 3 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2020 2021 Solutions. All Rs Aggarwal 2020 2021 Solutions for class Class 7 Maths are prepared by experts and are 100% accurate.

Page No 39:

Answer:

We have:

(i) $0.8 = \frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5}$

(ii) $0.75 = \frac{75}{100} = \frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

(iii) $0.06 = \frac{6}{100} = \frac{6 \div 2}{100 \div 2} = \frac{3}{50}$

(iv) $0.285 = \frac{285}{1000} = \frac{285 \div 5}{1000 \div 5} = \frac{57}{200}$

Page No 39:

Answer:

We have:

(i) $5.6 = \frac{56}{10} = \frac{56 \div 2}{10 \div 2} = \frac{28}{5} = 5 \frac{3}{5}$

(ii) $12.25 = \frac{1225}{100} = \frac{1225 \div 25}{100 \div 25} = \frac{49}{4} = 12 \frac{1}{4}$

(iii) $6.004 = \frac{6004}{1000} = \frac{6004 \div 4}{1000 \div 4} = \frac{1501}{250} = 6 \frac{1}{250}$

(iv) $4.625 = \frac{4625}{1000} = \frac{4625 \div 125}{1000 \div 125} = \frac{37}{8} = 4 \frac{5}{8}$

Page No 39:

Answer:

(i) $\frac{47}{10}$
    On dividing, we get:


    ∴ $\frac{47}{10}$ = 4.7

(ii) $\frac{156}{100}$
On dividing, we get:


∴ $\frac{156}{100}$ = 1.56

(iii) $\frac{2516}{100}$
On dividing, we get:

∴ $\frac{2516}{100}$ = 25.16

(iv) $\frac{3524}{1000}$

On dividing, we get:

∴ $\frac{3524}{1000}$ = 3.524

(v) $\frac{25}{8}$
On dividing, we get:

∴ $\frac{25}{8}$ = 3.125

(vi) $3 \frac{2}{5} = \frac{17}{5}$
On dividing, we get:

∴ $\frac{17}{5}$ = 3.4

(vii) $2 \frac{2}{25} = \frac{52}{25}$
        On dividing, we get:


∴ $\frac{52}{25}$ = 2.08

(viii) $\frac{17}{20}$

       On dividing, we get:



       ∴ $\frac{17}{20}$ = 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 = $\frac{45}{10}$ cm = 4.5 cm

= 4.5 cm = $\frac{4.5}{100} m$ = 0.045 m

= 0.045 m = $\frac{0.045}{1000} km$ = 0.000045 km

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

Page No 39:

Answer:

We have:
(i) 8 paise = Rs $\frac{8}{100}$ = Rs 0.08

(ii) 9 rupees 75 paise = Rs $(9 + \frac{75}{100}) = Rs (9 + 0.75)$ = Rs 9.75

(iii) 8 rupees 5 paise = $Rs (8 + \frac{5}{100}) = Rs (8 + 0.05)$ = Rs 8.05

Page No 39:

Answer:

We have:

(i) 65 m = $\frac{65}{1000}$ km = 0.065 km
∴ 65 m = 0.065 km

(ii) 284 m = $\frac{284}{1000}$ km = 0.284 km

(iii) 3 km 5 m = $(3 + \frac{5}{1000}) = (3 + 0.005) = 3.005 km$

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 $\times$ 16 = 864
     ∴ 5.4 $\times$ 16 = 86.4                            [1 place of decimal]

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

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

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

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

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

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

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

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

Page No 44:

Answer:

(i) First, we will multiply 76 by 24.

∴ 76 $\times$ 24 = 1824
Sum of decimal places in the given numbers = (1 + 1) = 2
∴ 7.6 $\times$ 2.4 = 18.24     [2 places of decimal]

(ii) First, we will multiply 345 by 63.

∴ 345 $\times$ 63 = 21735
Sum of decimal places in the given numbers = (2 + 1) = 3
∴ 3.45 $\times$ 6.3 = 21.735     [3 places of decimal]

(iii) First, we will multiply 54 by 27.

∴ 54 $\times$ 27 = 1458
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.54 $\times$ 0.27 = 0.1458    [4 places of decimal]

(iv) First, we will multiply 568 by 49.

∴ 568 $\times$ 49 = 27832
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.568 $\times$ 4.9 = 2.7832    [4 places of decimal]

(v) First, we multiply 654 by 9.

∴ 654 $\times$ 9 = 5886
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 6.54 $\times$ 0.09 = 0.5886     [4 places of decimal]

(vi) First, we will multiply 387 by 125.

∴ 387 $\times$ 125 = 48375
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 3.87 $\times$ 1.25 = 4.8375    [4 places of decimal]

(vii) First, we will multiply 38 by 6.

∴ 38 $\times$ 6 = 228
Sum of decimal places in the given numbers = (2 + 2) = 4
∴ 0.06 $\times$ 0.38 = 0.0228    [4 places of decimal]

(viii) First, we will multiply 623 by 75.

∴ 623 $\times$ 75 = 46725
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.623 $\times$ 0.75 = 0.46725    [5 places of decimal]

(ix) First, we will multiply 14 by 46.

∴ 14 $\times$ 46 = 644
Sum of decimal places in the given numbers = (3 + 2) = 5
∴ 0.014 $\times$ 0.46 = 0.00644    [5 places of decimal]

(x) First, we will multiply 545 by 176.

∴ 545 $\times$ 176 = 95920
Sum of decimal places in the given numbers = (1 + 2) = 3
∴ 54.5 $\times$ 1.76 = 95.920 [3 places of decimal]
                       = 95.92

(xi) First, we will multiply 45 by 24.

∴ 45 $\times$ 24 = 1080
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 0.045 $\times$ 2.4 = 0.1080    [4 places of decimal]
                       = 0.108

(xii) First, we will multiply 1245 by 64.

∴ 1245 $\times$ 64 = 79680
Sum of decimal places in the given numbers = (3 + 1) = 4
∴ 1.245 $\times$ 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 $\times$ 1.2
     First, we will find the product 1.2 $\times$ 1.2.
     Now, 12 $\times$ 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 $\times$ 1.2 = 1.44

(ii) (0.7)² = 0.7 $\times$ 0.7
      First, we will find the product 0.7 $\times$ 0.7.
      Now, 7 $\times$ 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 $\times$ 0.7 = 0.49

(iii) (0.04)² = 0.04 $\times$ 0.04
       First, we will find the product 0.04 $\times$ 0.04.
       Now, 4 $\times$ 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 $\times$ 0.04 = 0.0016

(iv) (0.11)² = 0.11 $\times$ 0.11
       First, we will find the product 0.11 $\times$ 0.11.
       Now, 11 $\times$ 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 $\times$ 0.11 = 0.0121

Page No 44:

Answer:

(i) (0.3)³ = 0.3 $\times$ 0.3 $\times$ 0.3
     First, we will find the product 3 $\times$ 3 $\times$ 3.
     Now, 3 $\times$ 3 $\times$ 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 $\times$ 0.3 $\times$ 0.3 = 0.027

(ii) (0.05)³ = 0.05 $\times$ 0.05 $\times$ 0.05
     First, we will find the product 5 $\times$ 5 $\times$ 5.
     Now, 5 $\times$ 5 $\times$ 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 $\times$ 0.05 $\times$ 0.05 = 0.000125

(iii) (1.5)³ = 1.5 $\times$ 1.5 $\times$ 1.5
       First, we will find the product 15 $\times$ 15 $\times$ 15.
       Now, 15 $\times$ 15 $\times$ 15 = 225 $\times$ 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 $\times$ 1.5 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 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 = $\frac{131.6}{10} = 13.16$                 [Shift the decimal point to the left by 1 place]

(ii) 32.56 ÷ 10 = $\frac{32.56}{10} = 3.256$                     [Shift the decimal point to the left by 1 place]

(iii) 4.38 ÷ 10 = $\frac{4.38}{10} = 0.438$                        [Shift the decimal point to the left by 1 place]

(iv) 0.34 ÷ 10 = $\frac{0.34}{10} = 0.034$                        [Shift the decimal point to the left by 1 place]

(v) 0.08 ÷ 10 = $\frac{0.08}{10} = 0.008$                         [Shift the decimal point to the left by 1 place]

(vi) 0.062 ÷ 10 = $\frac{0.062}{10} = 0.0062$                  [Shift the decimal point to the left by 1 place]

Page No 49:

Answer:

We have the following:

(i) 137.2 ÷ 100 = $\frac{137.2}{100} = 1.372$                           [Shifting the decimal point to the left by 2 places]

(ii) 23.4 ÷ 100 = $\frac{23.4}{100} = 0.234$                               [Shifting the decimal point to the left by 2 places]

(iii) 4.7 ÷ 100 = $\frac{4.7}{100} = 0.047$                                [Shifting the decimal point to the left by 2 places]

(iv) 0.3 ÷ 100 = $\frac{0.3}{100} = 0.003$                                [Shifting the decimal point to the left by 2 places]

(v) 0.58 ÷ 100 = $\frac{0.58}{100} = 0.0058$                            [Shifting the decimal point to the left by 2 places]

(vi) 0.02 ÷ 100 = $\frac{0.02}{100} = 0.0002$                         [Shifting the decimal point to the left by 2 places]

Page No 49:

Answer:

We have the following:

(i) 1286.5 ÷ 1000 = $\frac{1286.5}{1000} = 1.2865$              [Shift the decimal point to the left by 3 places]

(ii) 354.16 ÷ 1000 = $\frac{354.16}{1000} = 0.35416$               [Shift the decimal point to the left by 3 places]

(iii) 38.9 ÷ 1000 = $\frac{38.9}{1000} = 0.0389$                       [Shift the decimal point to the left by 3 places]

(iv) 4.6 ÷ 1000 = $\frac{4.6}{1000} = 0.0046$                         [Shift the decimal point to the left by 3 places]

(v) 0.8 ÷ 1000 = $\frac{0.8}{1000} = 0.0008$                          [Shift the decimal point to the left by 3 places]

(vi) 2 ÷ 1000 = $\frac{2}{1000} = 0.002$                          [Shift the decimal point to the left by 3 places]

Page No 49:

Answer:

(i) 12 ÷ 8 = $\frac{12}{8} = \frac{3}{2}$


∴ 12 ÷ 8 = 1.5

(ii) 63 ÷ 15 = $\frac{63}{15} = \frac{21}{5}$

   ∴ 63 ÷ 15 = 4.2

(iii) 47 ÷ 20 = $\frac{47}{20}$

        ∴ 47 ÷ 20 = 2.35

(iv) 101 ÷ 25 = $\frac{101}{25}$

       ∴ 101 ÷ 25 = 4.04

(v ) 31 ÷ 40


    ∴ 31 ÷ 40 = 0.775

(vi) 11 ÷ 16 = $\frac{11}{16}$


       ∴ 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

$= \frac{0.175}{25} = \frac{0.175 \times 1000}{25 \times 1000} = \frac{175}{25 \times 1000} = \frac{7}{1000} = 0.007$

(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 = $\frac{16.46}{20} = \frac{16.46 \times 100}{20 \times 100} = \frac{1646}{2 \times 1000} = \frac{823}{1000} = 0.823$

(ii) 403.8 ÷ 30 = $\frac{403.8}{30} = \frac{403.8 \times 10}{30 \times 10} = \frac{4038}{3 \times 100} = \frac{1346}{100} = 13.46$

(iii) 19.2 ÷ 80 = $\frac{19.2}{80} = \frac{19.2 \times 10}{80 \times 10} = \frac{192}{800} = \frac{192}{8 \times 100} = \frac{24}{100} = 0.24$

(iv) 156.8 ÷ 200 = $\frac{156.8}{200} = \frac{156.8 \times 10}{200 \times 10} = \frac{1568}{2000} = \frac{784}{1000} = 0.784$

(v) 12.8 ÷ 500 = $\frac{12.8}{500} = \frac{12.8 \times 10}{500 \times 10} = \frac{128}{5000} = \frac{25.6}{1000} = 0.0256$

(vi) 18.08 ÷ 400 = $\frac{18.08}{400} = \frac{18.08 \times 100}{400 \times 100} = \frac{1808}{40000} = \frac{452}{10000} = 0.0452$

Page No 49:

Answer:

(i) 3.28 ÷ 0.8 = $\frac{3.28}{0.8} = \frac{3.28 \times 10}{0.8 \times 10} = \frac{32.8}{8}$
Now, we have:


       ∴ $\frac{3.28}{0.8} = \frac{32.8}{8} = 4.1$

(ii)  0.288 ÷ 0.9 = $\frac{0.288}{0.9} = \frac{0.288 \times 10}{0.9 \times 10} = \frac{2.88}{9}$
Now, we have:


      ∴ $\frac{0.288}{0.9} = \frac{2.88}{9} = 0.32$

(iii)  25.395 ÷ 1.5 = $\frac{25.395}{1.5} = \frac{25.395 \times 10}{1.5 \times 10} = \frac{253.95}{15}$
Now, we have:


       ∴ $\frac{25.395}{1.5} = \frac{253.95}{15} = 16.93$

(iv) 2.0484 ÷ 0.18 = $\frac{2.0484}{0.18} = \frac{2.0484 \times 100}{0.18 \times 100} = \frac{204.84}{18}$
Now, we have:


     ∴ $\frac{2.0484}{0.18} = \frac{204.84}{18} = 11.38$

(v) 0.228 ÷ 0.38 = $\frac{0.228}{0.38} = \frac{0.228 \times 100}{0.38 \times 100} = \frac{22.8}{38}$
Now, we have:


     ∴ $\frac{0.228}{0.38} = \frac{22.8}{38} = 0.6$

(vi) 0.8085 ÷ 0.35 = $\frac{0.8085}{0.35} = \frac{0.8085 \times 100}{0.35 \times 100} = \frac{80.85}{35}$
Now, we have:


      ∴ $\frac{0.8085}{0.35} = \frac{80.85}{35} = 2.31$

(vii) 21.976 ÷ 1.64 = $\frac{21.976}{1.64} = \frac{21.976 \times 100}{1.64 \times 100} = \frac{2197.6}{164}$
Now, we have:

        ∴ $\frac{21.976}{1.64} = \frac{2197.6}{164} = 13.4$

(viii) 11.04 ÷ 1.6 = $\frac{11.04}{1.6} = \frac{11.04 \times 10}{1.6 \times 10} = \frac{110.4}{16}$
Now, we have:


       ∴ $\frac{11.04}{1.6} = \frac{110.4}{16} = 6.9$

(ix)  6.612 ÷ 11.6 = $\frac{6.612}{11.6} = \frac{6.612 \times 10}{11.6 \times 10} = \frac{66.12}{116}$
Now, we have:

       ∴ $\frac{6.612}{11.6} = \frac{66.12}{116} = 0.57$

(x) 0.076 ÷ 0.19 = $\frac{0.076}{0.19} = \frac{0.076 \times 100}{0.19 \times 100} = \frac{7.6}{19}$
Now, we have:

    ∴ $\frac{0.076}{0.19} = \frac{7.6}{19} = 0.4$

(xi) 48 ÷ 0.074

$= \frac{148}{0.074} = \frac{148 \times 1000}{0.074 \times 1000} = \frac{148000}{74} = 2 \times 1000 = 2000$

(xii)  16.578 ÷ 5.4 = $\frac{16.578}{5.4} = \frac{16.578 \times 10}{5.4 \times 10} = \frac{165.78}{54}$
Now, we have:


        ∴ $\frac{16.578}{5.4} = \frac{165.78}{54} = 3.07$

(xiii)  28 ÷ 0.56

$= \frac{28}{0.56} = \frac{28 \times 100}{0.56 \times 100} = \frac{2800}{56} = \frac{1 \times 100}{2} = 50$

(xiv) 204 ÷ 0.17

$= \frac{204}{0.17} = \frac{204 \times 100}{0.17 \times 100} = \frac{20400}{17} = 12 \times 100 = 1200$

(xv) 3 ÷ 80 = $\frac{3}{80}$

Now, we have:


       ∴ $\frac{3}{80}$ = 0.0375

Page No 50:

Answer:

Cost of 24 chairs = Rs 9255.60
∴ Cost of one chair = Rs $(\frac{9255.60}{24})$
= Rs $(\frac{9255.60 \times 10}{24 \times 10})$
= Rs $(\frac{92556}{240})$
= 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 = $\frac{45}{1.8}$ = $\frac{15}{0.6}$ = $\frac{5}{0.2}$ = $\frac{50}{2}$ = 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 = $(\frac{22.8}{2.4})$ km
= $(\frac{228}{24})$ km = $(\frac{228 \div 12}{24 \div 12})$ km = $(\frac{19}{2})$ km = $9 \frac{1}{2}$ km

Hence, the distance covered by the car with 1 litre of petrol is $9 \frac{1}{2}$ 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 = $(\frac{478.5}{16.5}) = (\frac{4785}{165}) = (\frac{4785 \div 15}{165 \div 15}) = \frac{319}{11} = 29$
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 = $(\frac{3644.5}{37})$ = 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 = $(\frac{586.5}{69})$ 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 = $(\frac{46}{1.15})$
= $(\frac{46 \times 100}{1.15 \times 100})$ = $(\frac{4600}{115})$ = 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 = $(\frac{Total weight}{Weight of each bag})$
= $(\frac{1792.8}{49.8}) = (\frac{17928}{498}) = 36$

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 = $(\frac{189}{0.35}) = (\frac{189 \times 100}{0.35 \times 100}) = (\frac{18900}{35}) = 540$

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
= $(\frac{261.36}{17.6}) = (\frac{261.36 \times 10}{17.6 \times 10}) = (\frac{2613.6}{176})$
= 14.85

Hence, the other decimal is 14.85.

Page No 50:

Answer:

(b) $\frac{3}{50}$

0.06 = $\frac{6}{100} = \frac{3}{50}$

Page No 50:

Answer:

Page No 50:

Answer:

(b) 2.08

$2 \frac{2}{25} = \frac{52}{25}$

On dividing, we get:

∴ $2 \frac{2}{25} = \frac{52}{25}$ = 2.08

Page No 50:

Answer:

Page No 50:

Answer:

(b) 0.07 kg

70 g = $\frac{70}{1000}$ kg = $\frac{7}{100}$ kg

= 0.07 kg

∴ 70 g = 0.07 kg

Page No 50:

Answer:

Page No 50:

Answer:

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 $\times$ 3 = 69
Sum of decimal places in the given decimals = (2 + 1) = 3
∴ 0.23 $\times$ 0.3 = 0.069 ( 3 places of decimal)

Page No 51:

Answer:

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

Page No 51:

Answer:

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

Page No 51:

Answer:

(c) .064

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

Page No 51:

Answer:

(a) 13

2.08 ÷ 0.16 = $\frac{2.08}{0.16}$ = $\frac{2.08 \times 100}{0.16 \times 100}$ = $\frac{208}{16} = 13$

Page No 51:

Answer:

(b) 0.17

1.02 ÷ 6 = $\frac{1.02}{6} = \frac{1.02 \times 100}{6 \times 100} = \frac{102}{6 \times 100} = \frac{17}{100} = 0.17$

Page No 51:

Answer:

(a) 44.2

30.94 ÷ 0.7 = $\frac{30.94}{0.7} = \frac{30.94 \times 100}{0.7 \times 100} = \frac{3094}{70} = 44.2$

Page No 51:

Answer:

(b) 2.1

2.73 ÷ 1.3 = $\frac{2.73}{1.3} = \frac{2.73 \times 100}{1.3 \times 100} = \frac{273}{13 \times 10} = \frac{21}{10} = 2.1$

Page No 51:

Answer:

(a) 40.5

89.1 ÷ 2.2 = $\frac{89.1}{2.2} = \frac{89.1 \times 10}{2.2 \times 10} = \frac{891}{22} = 40.5$

Page No 51:

Answer:

(c) 0.025
First, we will multiply 5 by 5.
i.e., 5 $\times$ 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 $\times$ 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 $\times$ 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 $\times$ 65 $\times$ 4.
Now, 68 $\times$ 65 $\times$ 4 = 4420 $\times$ 4 = 17680
Sum of decimal places in the given decimals = (2 + 1 + 2) = 5
So, the product have five decimal places.

∴ 0.68 $\times$ 6.5 $\times$ 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 = $\frac{Total weight}{Weight of each bag}$

= $(\frac{2231}{48.5})$ kg

= $(\frac{2231 \times 10}{48.5 \times 10}) = \frac{22310}{485} = 46$

Hence, 46 bags of cement will weigh 2231 kg.

Page No 53:

Answer:

(i) 0.196 ÷ 1.4 = $\frac{0.196}{1.4} = \frac{0.196 \times 10}{1.4 \times 10} = \frac{1.96}{14} = 0.14$



(ii) 39.168 ÷ 1.2 = $\frac{39.168}{1.2} = \frac{39.168 \times 10}{1.2 \times 10} = \frac{391.68}{12} = 32.64$



(iii) 0.228 ÷ 0.38 = $\frac{0.228}{0.38} = \frac{0.228 \times 100}{0.38 \times 100} = \frac{22.8}{38} = 0.6$

Page No 53:

Answer:

Product of the given decimals = 1.824
One decimal = 0.64
The other decimal = 1.824 ÷ 0.64
= $\frac{1.824}{0.64} = (\frac{1.824 \times 100}{0.64 \times 100}) = \frac{182.4}{64} = 2.85$

Hence, the other decimal is 2.85.

Page No 53:

Answer:

Thickness of the pile of plywoods = 2.43 m = 2.43 $\times$ 100 cm = 243 cm
Thickness of one piece of plywood = 0.45 cm
∴ Required number of pieces of plywood = $\frac{243}{0.45} = \frac{243 \times 100}{0.45 \times 100} = \frac{24300}{45} = 540$

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 $\times$ n) cm
But it is given that its perimeter is 22.8 cm.
∴ (3.8 $\times$ n) cm = 22.8 cm
⇒ n = $(\frac{22.8}{3.8})$ = $\frac{228}{38}$ = 6

Hence, the given polygon has six sides.

Page No 53:

Answer:

(b) 2.04

$2 \frac{1}{25} = \frac{51}{25} = 2.04$

Page No 53:

Answer:

(b) $1 \frac{1}{125}$

1.008 = $\frac{1.008 \times 1000}{1 \times 1000} = \frac{1008}{1000} = \frac{1008 \div 4}{1000 \div 4} = \frac{126}{125} = 1 \frac{1}{125}$

Page No 53:

Answer:

Page No 53:

Answer:

(b) 0.08

We have:
0.012 ÷ 0.15 = $\frac{0.012}{0.15} = \frac{0.012 \times 100}{0.15 \times 100} = \frac{1.2}{15} = 0.08$

Page No 53:

Answer:

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

∴ 1.1 $\times$ 0.1 $\times$ 0.01 = 0.0011 [4 places of decimal]

Page No 53:

Answer:

(b) 2.03

4.669 ÷ 2.3 = $(\frac{4.669}{2.3}) = (\frac{4.669 \times 10}{2.3 \times 10}) = (\frac{46.69}{23}) = 2.03$

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: $\frac{1.001}{14} = 0.0715$


(ii) 204 ÷ 0.17 = 1200

      Explanation: $\frac{204}{0.17} = \frac{204 \times 100}{0.17 \times 100} = \frac{204 \times 100}{17} = 12 \times 100 = 1200$

(iii) 0.47 × 5.3 = 2.491

       Explanation: First, we will multiply 47 by 53.

        ∴ 47 $\times$ 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 = $\frac{0.35}{0.7} = \frac{0.35 \times 10}{0.7 \times 10} = \frac{3.5}{7} = 0.5$

(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 = $(\frac{6}{100})$ m = 0.06 m

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