RS Aggrawal 2020 2021 Solutions for Class 6 Maths Chapter 7 - Decimals

Question 1:

Question 2:

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

Question 3:

(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 = $\frac{8}{10}$
Place value of 3 = 3 hundredths = $\frac{3}{100}$

(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 = $\frac{2}{10}$
Place value of 6 = 6 hundredths = $\frac{6}{100}$
Place value of 9 = 9 thousandths = $\frac{9}{1000}$

(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 = $\frac{0}{10}$= 0
Place value of 7 = 7 hundredths = $\frac{7}{100}$
Place value of 5 = 5 thousandths = $\frac{5}{1000}$

(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 = $\frac{4}{10}$
Place value of 5 = 5 hundredths = $\frac{5}{100}$
Place value of 9 = 9 thousandths = $\frac{9}{1000}$

(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 = $\frac{3}{10}$
Place value of 4 = 4 hundredths = $\frac{4}{100}$

(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 = $\frac{2}{10}$
Place value of 0 = 0 hundredths = 0
Place value of 9 = 9 thousandths = $\frac{9}{1000}$

Question 4:

(i) 67.83
 = 6 tens + 7 ones + 8 tenths + 3 hundredths
 = $60 + 7 + \frac{8}{10} + \frac{3}{100}$

(ii) 283.61
 = 2 hundreds  + 8 tens + 3 ones + 6 tenths + 1 hundredths
 = $200 + 80 + 3 + \frac{6}{10} + \frac{1}{100}$

(iii) 24.675
 = 2 tens + 4 ones + 6 tenths + 7 hundredths + 5 thousandths
 = $20 + 4 + \frac{6}{10} + \frac{7}{100} + \frac{5}{1000}$

(iv) 0.294
 = 2 tenths + 9 hundredths + 4 thousandths
 = $\frac{2}{10} + \frac{9}{100} + \frac{4}{1000}$

(v) 8.006
 = 8 ones + 0 tenths + 0 hundredths  + 6 thousandths
 = $8 + \frac{0}{10} + \frac{0}{100} + \frac{6}{1000}$

(vi) 4615.72
 = 4 thousands + 6 hundreds + 1 tens + 5 ones + 7 tenths + 2 hundredths
 = $4000 + 600 + 10 + 5 + \frac{7}{10} + \frac{2}{100}$

Question 5:

(i) $40 + 6 + \frac{7}{10} + \frac{9}{100}$ = 46 + 0.7 + .09 = 46.79

(ii) $500 + 70 + 8 + \frac{3}{10} + \frac{1}{100} + \frac{6}{1000}$ = 578 + 0.3 + 0.01 + 0.006 = 578.316

(iii) $700 + 30 + 1 + \frac{8}{10} + \frac{4}{100}$ = 731 + 0.8 + 0.04 = 731.84

(iv) $600 + 5 + \frac{7}{100} + \frac{9}{1000}$ = 605 + 0.07 + 0.009 = 605.079

(v) $800 + 5 + \frac{8}{10} + \frac{6}{1000}$ = 805 + 0.8 + 0.006 = 805.806

(vi) $30 + 9 + \frac{4}{100} + \frac{8}{1000}$ = 39 + 0.04 + 0.008 = 39.048

Question 6:

(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

Question 7:

(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)

Question 8:

(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

Question 1:

(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

Question 2:

We have:
 .9 = $\frac{9}{10}$

Question 3:

We have:
 0.6 = $\frac{6}{10} = \frac{3}{5}$

Question 4:

We have:
 0.08 = $\frac{8}{100} = \frac{4}{50} = \frac{2}{25}$
    

Question 5:

We have:
 0.15 = $\frac{15}{100} = \frac{3}{20}$

Question 6:

We have:
 0.48 = $\frac{48}{100} = \frac{12}{25}$

Question 7:

We have:
 0.053 = $\frac{53}{1000}$

Question 8:

We have:
 0.125 = $\frac{125}{1000} = \frac{25}{200} =\frac{5}{40}= \frac{1}{8}$

Question 9:

We have:
0.224 = $\frac{224}{1000} = \frac{56}{250} = \frac{28}{125}$

Question 10:

We have:
 6.4 = $\frac{64}{10} = \frac{32}{5} = 6\frac{2}{5}$

Question 11:

We have:
 16.5 = $\frac{165}{10} = \frac{33}{2} =16\frac{1}{2}$

Question 12:

We have:
 8.36 = $\frac{836}{100} = \frac{209}{25} = 8\frac{9}{25}$

Question 13:

We have:
 4.275 = $\frac{4275}{1000} = \frac{171}{40} = 4\frac{11}{40}$

Question 14:

We have:
 25.06 = $\frac{2506}{100} = \frac{1253}{50} =25\frac{3}{50}$

Question 15:

We have:
7.004 = $\frac{7004}{1000} = \frac{1751}{250} = 7\frac{1}{250}$

Question 16:

We have:
2.052 = $\frac{2052}{1000} = \frac{513}{250} = 2\frac{13}{250}$

Question 17:

We have:
3.108 = $\frac{3108}{1000} = \frac{777}{250} = 3\frac{27}{250}$

Question 18:

We have:
$\frac{23}{10} = 2\frac{3}{10} = 2 + 0.3 = 2.3$

Question 19:

We have:
$\frac{167}{100} = 1\frac{67}{100} = 1 + 0.67 = 1.67$

Question 20:

We have:
$\frac{1589}{100} = 15\frac{89}{100} = 15+ 0.89 = 15.89$

Question 21:

We have:
$\frac{5413}{1000} = 5\frac{413}{1000} = 5 + 0.413 = 5.413$

Question 22:

We have:
$\frac{21415}{1000} = 21\frac{415}{1000} = 21 + 0.415 = 21.415$

Question 23:

We have:
$\frac{25}{4} = 6\frac{1}{4} = 6 + 0.25 = 6.25$

Question 24:

We have:
$3\frac{3}{5}= 3 + 0.6 = 3.6$

Question 25:

We have:
$1\frac{4}{25} = 1 + 0.16 = 1.16$

Question 26:

We have:
$5\frac{17}{50} = 5 + 0.34 = 5.34$

Question 27:

We have:
$12\frac{3}{8} = 12 + 0.375 = 12.375$

Question 28:

We have:
$2\frac{19}{40} = 2 + 0.475 = 2.475$

Question 29:

We have:
$\frac{19}{20} = 0.95$

Question 30:

We have:
$\frac{37}{50} = 0.74$

Question 31:

We have:
$\frac{107}{250} = 0.428$

Question 32:

We have:
$\frac{3}{40} = 0.075$

Question 33:

We have:
$\frac{7}{8} = 0.875$

Question 34:

(i) 8 kg 640 g in kilograms:
     8 kg + 640 gm = 8 kg + $\frac{640}{1000}$ kg
     8 kg + 0.640 kg = 8.640 kg

(ii) 9 kg 37 g in kilograms:
     9 kg + 37 gm = 9 kg + $\frac{37}{1000}$ kg
     9 kg + 0.037 kg = 9.037 kg

(iii) 6 kg 8 g in kilograms:
      6 kg + 8 gm = 6 kg + $\frac{8}{1000}$ kg
      6 kg + 0.008 kg = 6.008 kg

Question 35:

(i) 4 km 365 m in kilometres:
    4 km + 365 m = 4 km + $\frac{365}{1000}$ 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 + $\frac{87}{1000}$ 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 + $\frac{6}{1000}$ km      [Since 1 km = 1000 m]
     3 km + 0.006 km = 3.006 km

(iv) 270 m in kilometres:
      $\frac{270}{1000}$ km = 0.270 km                     [Since 1 km = 1000 m]

(v) 35 m in kilometres:
      $\frac{35}{1000}$ km = 0.035 km                      [Since 1 km = 1000 m]

(vi) 6 m in kilometres:
       $\frac{6}{1000}$ km = 0.006 km                    [Since 1 km = 1000 m]

Question 36:

(i) 15 kg 850 g in kilograms:
    15 kg + 850 gm = 15 kg + $\frac{850}{1000}$ 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 + $\frac{96}{1000}$kg         [Since 1 kg = 1000 gm]
     8 kg + 0.096 kg = 8.096 kg

(iii) 540 g in kilograms:
       540 gm = $\frac{540}{1000}$ kg = 0.540 kg        [Since 1 kg = 1000 gm]

(iv) 8 g in kilograms:
       8 gm = $\frac{8}{1000}$ kg = 0.008 kg           [Since 1 kg = 1000 gm]

Question 1:

(i) Rs 18 and 25 paise in rupees:
    Rs 18 + 25 paise = Rs 18 + Rs $\frac{25}{100}$         [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 $\frac{8}{100}$         [Since Re 1 = 100 paise]
    Rs 9 + Rs 0.08 = Rs 9.08

(iii) 32 paise in rupees:
      32 paise = Rs $\frac{32}{100}$ = Rs 0.32          [Since Re 1 = 100 paise]

(iv) 5 paise in rupees:
      5 paise = Rs $\frac{5}{100}$ = Rs 0.05          [Since Re 1 = 100 paise]

Question 2:

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.

Question 3:

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.

Question 4:

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.

Question 5:

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.

Question 6:

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.

Question 7:

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.

Question 8:

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.

Question 9:

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.

Question 10:

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

Question 11:

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    

Question 12:

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

Question 13:

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

Question 14:

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

Question 1:

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

Question 2:

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

Question 3:

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

Question 4:

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
$\therefore$ 53.74 - 27.86 = 32.77

Question 5:

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
$\therefore$ 204.00 - 56.80 = 147.2

Question 6:

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
$\therefore$ 216.20 - 127.38 = 88.82

Question 7:

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
$\therefore$ 70.680 - 39.875 = 30.805

Question 8:

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
$\therefore$ 523.120 - 348.237 = 174.883

Question 9:

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
$\therefore$ 600.000 - 458.573 =141.427

Question 10:

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

Question 11:

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
$\therefore$ 3.400 - 0.612 = 2.788

Question 12:

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                     

Question 13:

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
                                 
                              

Question 14:

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
                                 
                              

Question 15:

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
                                 
                              

Question 16:

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.

Question 17:

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.

Question 18:

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

Question 19:

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

Question 20:

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.

Question 21:

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.

Question 22:

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.

Question 1:

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

$\therefore$ Distance covered by walking = 0.860 km = 860 metres

Question 2:

(c) 0.7

$\frac{7}{10}$ = 7 tenths = 0.7

Question 3:

(d) 0.05
 $\frac{5}{100}$ = 5 hundredths = 0.05

Question 4:

(b) 0.009
$\frac{9}{1000}$ = 9 thousandths = 0.009

Question 5:

(a) 0.016
$\frac{16}{1000}$ = 16 thousandths = 0.016

Question 6:

(c) 0.134
 $\frac{134}{1000}$ = 134 thousandths = 0.134

Question 7:

(a) 2.17
 2$\frac{17}{100}$ = 2 + $\frac{17}{100}$ = 2 + 0.17 = 2.17

Question 8:

(b) 4.03
 4$\frac{3}{100}$ = 4 + $\frac{3}{100}$ = 4 + 0.03 = 4.03

Question 9:

b) $6\frac{1}{4}$614
6.25 = 6 + 0.25 = 6 + $\frac{25}{100}$ = 6 + $\frac{1}{4}$ = $6\frac{1}{4}$

Question 10:

(b) 0.24
     $\frac{6}{25}$ =  0.24
                                  
            25) 60 (0.24
               $-$50
                  100
              $-$ 100
                   0  

Question 11:

(c) 4.875
$4\frac{7}{8}$ =  4 + $\frac{7}{8}$ = 4 + 0.875 = 4.875

Question 12:

(a)  $24\frac{4}{5}$
24.8 = 24 + 0.8 = 24 + $\frac{8}{10}$ = 24 + $\frac{4}{5}$ = $24\frac{4}{5}$

Question 13:

(b) 2.04
$2\frac{1}{25}$ = 2 + $\frac{1}{25}$ = 2 + 0.04 = 2.04

Question 14:

(c) 2.34
2 + $\frac{3}{10} + \frac{4}{100}$ = 2 + 0.3 + 0.04 = 2.34

Question 15:

(b) 2.06
2 + $\frac{6}{100}$ = 2 + 0.06 = 2.06

Question 16:

(c) 0.0407
$\frac{4}{100} + \frac{7}{10000}$ = 0.04 + 0.0007 = 0.0407

Question 17:

(c) $(2 \times 1) + (6 \times \frac{1}{100})$

2.06 =  2 + $\frac{6}{100}$ = $(2 \times 1) + (6 \times \frac{1}{100})$2 × 1) + (6 × 1(2 × 1) + (6 (2 × 1) + (6 

Question 18:

(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.

Question 19:

(b) 2.002 < 2.02 < 2.2 < 2.222

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

$\therefore$ 2.002 < 2.02 < 2.2 < 2.222

Question 20:

(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.

Question 21:

(b) 0.01 m
1 m = 100 cm
$\therefore$ 1 cm = $\frac{1}{100}$m = 0.01 m   

Question 22:

(b) 2.05 m
2 m 5 cm = (2 + $\frac{5}{100}$) m = (2 + 0.05) m = 2.05 m

Question 23:

(c) 2.008 kg
1 kg = 1000 g
$\therefore$ 2 kg 8 g = 2 kg + $\frac{8}{1000}$ kg = (2 + 0.008) kg = 2.008 kg

Question 24:

(b) 2.056 kg
2 kg + 56 g = (2 + $\frac{56}{1000}$) kg = (2 + 0.056) kg = 2.056 kg

Question 25:

(c) 2.035 km
1 km = 1000 m
$\therefore$ 2 km 35 m  = (2 + $\frac{35}{1000}$) km = (2 + 0.035) km = 2.035 km

Question 26:

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

Question 27:

(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

Question 28:

(b) 3.5

   6.3
− 2.8
   3.5

Question 29:

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

Question 30:

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

Question 1:

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

Question 2:

$4\frac{5}{8}$ = 4 + $\frac{5}{8}$ =  4 + 0.625 = 4.625

Question 3:

1 cm = $\frac{1}{100}$ m
$\therefore$ 105 cm = $\frac{105}{100}$ m = (1 + $\frac{5}{100}$) m = (1 + 0.05) m = 1.05 m

Question 4:

1 m = $\frac{1}{1000}$ km
  $\therefore$ 5 m = $\frac{5}{1000}$ km = 0.005 km
6 km 5 m = (6 + 0.005) km = 6.005 km

Question 5:

1 m = $\frac{1}{1000}$ km
$\therefore$8 m = $\frac{8}{1000}$ km = 0.008 km

Question 6:

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

Question 7:

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

Question 8:

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

Question 9:

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.

Question 10:

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

Question 11:

(i) 0.4 = $\frac{4}{10} = \frac{2}{5}$

(ii) 0.35 = $\frac{35}{100} = \frac{7}{20}$

(iii) 0.08 = $\frac{8}{100} = \frac{2}{25}$

(iv) 0.075 = $\frac{75}{1000} = \frac{3}{40}$

Question 12:

(b) 0.12
 $\frac{3}{25}$ = 0.12
                  
      25)  30 (0.12
         $-$25
               50
           $-$ 50  
                 0  

Question 13:

(c) 0.006
 $\frac{6}{1000}$ = 6 thousandths = 0.006

Question 14:

(b) 2.03
$2\frac{3}{100}$ = 2 + $\frac{3}{100}$ = 2 + 0.03 = 2.03

Question 15:

(b) $\frac{3}{100}$
 In 16.534, place value of 3 = 3 hundredths = 0.03 = $\frac{3}{100}$

Question 16:

(c) 4.875
$4\frac{7}{8}$ = 4 + $\frac{7}{8}$ = 4 + 0.875 = 4.875

Question 17:

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

Question 18:

(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

Question 19:

(c) 0.0407

  $\frac{4}{100} + \frac{7}{10000}$ = 0.04  + 0.0007
Converting into like decimals:
0.0400 + 0.0007 = 0.0407

Question 20:

(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.

Question 21:

(i) 1 m = $\frac{1}{1000}$ km = 0.001 km

(ii) 10 mL = $\frac{1}{100}$ 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.