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Question 1:

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

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

Question 2:

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

(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 3:

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

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

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

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

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

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

(vi) 4615.72
= 4 thousands + 6 hundreds + 1 tens + 5 ones + 7 tenths + 2 hundredths
=

Question 4:

Write each of the following in decimals form:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

(i) = 46 + 0.7 + .09 = 46.79

(ii) = 578 + 0.3 + 0.01 + 0.006 = 578.316

(iii) = 731 + 0.8 + 0.04 = 731.84

(iv) = 605 + 0.07 + 0.009 = 605.079

(v) = 805 + 0.8 + 0.006 = 805.806

(vi) = 39 + 0.04 + 0.008 = 39.048

Question 5:

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

(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 6:

Fill in each of the place holders with the correct symbol > or <:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

(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 7:

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

(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 8:

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

(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 1:

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

We have:
.9 = $\frac{9}{10}$

Question 2:

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

We have:
0.6 =

Question 3:

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

We have:
0.08 =

Question 4:

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

We have:
0.15 =

Question 5:

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

We have:
0.48 =

Question 6:

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

We have:
0.053 =

Question 7:

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

We have:
0.125 =

Question 8:

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

We have:
0.224 =

Question 9:

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

We have:
6.4 =

Question 10:

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

We have:
16.5 =

Question 11:

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

We have:
8.36 =

Question 12:

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

We have:
4.275 =

Question 13:

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

We have:
25.06 =

Question 14:

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

We have:
7.004 =

Question 15:

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

We have:
2.052 =

Question 16:

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

We have:
3.108 =

Question 17:

Convert each of the following into a decimal:
$\frac{23}{10}$

We have:

Question 18:

Convert each of the following into a decimal:
$\frac{167}{100}$

We have:

Question 19:

Convert each of the following into a decimal:
$\frac{1589}{100}$

We have:

Question 20:

Convert each of the following into a decimal:
$\frac{5413}{1000}$

We have:

Question 21:

Convert each of the following into a decimal:
$\frac{21415}{1000}$

We have:

Question 22:

Convert each of the following into a decimal:
$\frac{25}{4}$

We have:

Question 23:

Convert each of the following into a decimal:
$3\frac{3}{5}$

We have:

Question 24:

Convert each of the following into a decimal:
$1\frac{4}{25}$

We have:

Question 25:

Convert each of the following into a decimal:
$5\frac{17}{50}$

We have:

Question 26:

Convert each of the following into a decimal:
$12\frac{3}{8}$

We have:

Question 27:

Convert each of the following into a decimal:
$2\frac{19}{40}$

We have:

Question 28:

Convert each of the following into a decimal:
$\frac{19}{20}$

We have:

Question 29:

Convert each of the following into a decimal:
$\frac{37}{50}$

We have:

Question 30:

Convert each of the following into a decimal:
$\frac{107}{250}$

We have:

Question 31:

Convert each of the following into a decimal:
$\frac{3}{40}$

We have:

Question 32:

Convert each of the following into a decimal:
$\frac{7}{8}$

We have:

Question 33:

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

(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 34:

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

(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 35:

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

(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 + 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 36:

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

(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 1:

9.6, 14.8, 37 and 5.9

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.
9.6
14.8
37.0
5.9
67.3
Hence, the sum of the given numbers is 67.3.

Question 2:

23.7, 106.94, 68.9 and 29.5

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.
23.70
106.94
68.90
29.50
229.04
Hence, the sum of the given numbers is 229.04.

Question 3:

72.8, 7.68, 16.23 and 0.7

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.
72.80
7.68
16.23
0.70
97.41
Hence, the sum of the given numbers is 97.41.

Question 4:

18.6, 84.75, 8.345 and 9.7

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.
18.600
84.750
8.345
9.700
121.395
Hence, the sum of the given numbers is 121.395.

Question 5:

8.236, 16.064, 63.8 and 27.53

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.
8.236
16.064
63.800
27.530
115.630
Hence, the sum of the given numbers is 115.630.

Question 6:

28.9, 19.64, 123.697 and 0.354

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.
28.900
19.640
123.697
0.354
172.591
Hence, the sum of the given numbers is 172.591.

Question 7:

4.37, 9.638, 17.007 and 6.8

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.
4.370
9.683
17.007
6.800
37.815
Hence, the sum of the given numbers is 37.815.

Question 8:

14.5, 0.038, 118.573 and 6.84

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.
14.500
0.038
118.573
6.840
139.951
Hence, the sum of the given numbers is 139.951.

Question 9:

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

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 10:

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

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 11:

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

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 12:

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

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 13:

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

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 14:

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

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 1:

Subtract:
27.86 from 53.74

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 2:

Subtract:
64.98 from 103.87

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 3:

Subtract:
59.63 from 92.4

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 4:

Subtract:
56.8 from 204

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 5:

Subtract:
127.38 from 216.2

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 6:

Subtract:
39.875 from 70.68

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 7:

Subtract:
348.237 from 523.12

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 8:

Subtract:
458.573 from 600

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 9:

Subtract:
149.456 from 206.321

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 10:

Subtract:
0.612 from 3.4

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 11:

Simplify:
37.6 + 72.85 − 58.678 − 6.09

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 12:

Simplify:
75.3 − 104.645 + 178.96 − 47.9

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 13:

Simplify:
213.4 − 56.84 − 11.87 − 16.087

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 14:

Simplify:
76.3 − 7.666 − 6.77

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 15:

What is to be added to 74.5 to get 91?

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 16:

What is to be subtracted from 7.3 to get 0.862?

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 17:

By how much should 23.754 be increased to get 50?

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 18:

By how much should 84.5 be decreased to get 27.84?

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 19:

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

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 20:

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

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 21:

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

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 22:

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

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 1:

Mark (✓) against the correct answer in each of the following:
$\frac{7}{10}=?$
(a) 7.1
(b) 1.7
(c) 0.7
(d) 0.07

(c) 0.7

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

Question 2:

Mark (✓) against the correct answer in each of the following:
$\frac{5}{100}=?$
(a) 5.1
(b) 5.01
(c) 0.5
(d) 0.05

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

Question 3:

Mark (✓) against the correct answer in each of the following:
$\frac{9}{1000}=?$
(a) 0.0009
(b) 0.009
(c) 9.001
(d) none of these

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

Question 4:

Mark (✓) against the correct answer in each of the following:
$\frac{16}{1000}=?$
(a) 0.016
(b) 0.16
(c) 0.0016
(d) 1.006

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

Question 5:

Mark (✓) against the correct answer in each of the following:
$\frac{134}{1000}=?$
(a) 13.4
(b) 1.34
(c) 0.134
(d) 0.0134

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

Question 6:

Mark (✓) against the correct answer in each of the following:
$2\frac{17}{100}=?$
(a) 2.17
(b) 2.017
(c) 0.217
(d) 21.7

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

Question 7:

Mark (✓) against the correct answer in each of the following:
$4\frac{3}{100}=?$
(a) 4.3
(b) 4.03
(c) 4.003
(d) 43.10

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

Question 8:

Mark (✓) against the correct answer in each of the following:
6.25 = ?
(a) $6\frac{1}{2}$
(b) $6\frac{1}{4}$
(c) $62\frac{1}{2}$
(d) none of these

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

Question 9:

Mark (✓) against the correct answer in each of the following:
$\frac{6}{25}=?$
(a) 2.4
(b) 0.24
(c) 0.024
(d) none of these

(b) 0.24
$\frac{6}{25}$ =  0.24

25) 60 (0.24
$-$50
100
$-$ 100
0

Question 10:

Mark (✓) against the correct answer in each of the following:
$4\frac{7}{8}=?$
(a) 4.78
(b) 4.87
(c) 4.875
(d) none of these

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

Question 11:

Mark (✓) against the correct answer in each of the following:
24.8 = ?
(a) $24\frac{4}{5}$
(b) $24\frac{2}{5}$
(c) $24\frac{1}{5}$
(d) none of these

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

Question 12:

Mark (✓) against the correct answer in each of the following:
$2\frac{1}{25}=?$
(a) 2.4
(b) 2.04
(c) 2.004
(d) none of these

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

Question 13:

Mark (✓) against the correct answer in each of the following:
$2+\frac{3}{10}+\frac{4}{100}$
(a) 2.304
(b) 2.403
(c) 2.34
(d) none of these

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

Question 14:

Mark (✓) against the correct answer in each of the following:
$2+\frac{6}{100}=?$
(a) 2.006
(b) 2.06
(c) 2.6
(d) none of these

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

Question 15:

Mark (✓) against the correct answer in each of the following:
$\frac{4}{100}+\frac{7}{10000}=?$
(a) 0.47
(b) 0.407
(c) 0.0407
(d) none of these

(c) 0.0407
= 0.04 + 0.0007 = 0.0407

Question 16:

The correct expanded from of 2.06 is
(a)
(b)
(c)
(d) none of these

(c)

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

Question 17:

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

(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 18:

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

(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 19:

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

(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 20:

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

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

Question 21:

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

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

Question 22:

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

(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 23:

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

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

Question 24:

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

(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 25:

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

(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 26:

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

(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 27:

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

(b) 3.5

6.3
2.8
3.5

Question 28:

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

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

Question 29:

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

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

Question 30:

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

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

Question 1:

Convert $4\frac{5}{8}$ into a decimal fraction.

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

Question 2:

Express 105 cm into metres using decimals.

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 3:

Express 6 km 5 m as km using decimals.

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 4:

Express 8 m as kilometre using decimals.

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

Question 5:

Add 26.4, 163.05, 8.75 and 5.6.

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

Question 6:

Subtract 0.528 from 3.2.

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

Question 7:

What is to be added to 63.5 to get 71?

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 8:

What is to be subtracted from 13 to get 5.4?

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 9:

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

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 10:

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

(i) 0.4 =

(ii) 0.35 =

(iii) 0.08 =

(iv) 0.075 =

Question 11:

Mark (✓) against the correct answer in each of the following:
$\frac{3}{25}=?$
(a) 1.2
(b) 0.12
(c) 0.012
(d) none of these

(b) 0.12
$\frac{3}{25}$ = 0.12

25)  30 (0.12
$-$ 25
50
$-$ 50
0

Question 12:

Mark (✓) against the correct answer in each of the following:
$\frac{6}{1000}=?$
(a) 6.001
(b) 0.0006
(c) 0.006
(d) 0.06

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

Question 13:

Mark (✓) against the correct answer in each of the following:
$2\frac{3}{100}=?$
(a) 2.003
(b) 2.03
(c) 2.3
(d) none of these

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

Question 14:

Mark (✓) against the correct answer in each of the following:
The place value of 3 in 16.534 is
(a) $\frac{3}{10}$
(b) $\frac{3}{100}$
(c) $\frac{3}{1000}$
(d) 3

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

Question 15:

Mark (✓) against the correct answer in each of the following:
$4\frac{7}{8}=?$
(a) 4.78
(b) 4.87
(c) 4.875
(d) none of these

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

Question 16:

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

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

Question 17:

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

(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 18:

Mark (✓) against the correct answer in each of the following:
$\frac{4}{100}+\frac{7}{10000}=?$
(a) 0.47
(b) 0.407
(c) 0.0407
(d) none of these

(c) 0.0407

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

Question 19:

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

(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 20:

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

(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.

Question 21:

Write 'T' for true and 'F' for false for each of the statements given below:
(i) 3.02 < 3.2.
(ii) 3 g = 0.003 kg.
(iii) $\frac{341}{1000}=3.410.$
(iv) 6.2 and 6.200 are equivalent decimals.
(v) 2.3, 3.41, 4.53, 5.61 are examples of like decimals.

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

(ii) True
1 g = $\frac{1}{1000}$ kg
$\therefore$ 3 g = $\frac{3}{1000}$ = 0.003 kg

(iii) False
$\frac{341}{1000}$ = 0.341
This is because it is equal to 341 thousandths.

(iv) True

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

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