Decimals (Exercise 3.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

Q.1. Divide:

(i) 142.45 by 10

(ii) 54.25 by 10

(iii) 3.45 by 10

(iv) 0.57 by 10

(v) 0.043 by 10

(vi) 0.004 by 10

Ans: 

(i)

=

= 14.245

(ii)

=

= 5.425

(iii)

=

= 0.345

(iv)

= 0.057

(v)

= 0.0043

(vi)

= 0.0004

Q.2. Divide:

(i) 459.5 by 100

(ii) 74.3 by 100

(iii) 5.8 by 100

(iv) 0.7 by 100

(v) 0.48 by 100

(vi) 0.03 by 100

Ans: 

(i)

= 4.595 

(ii)

= 0.743

(iii)

= 0.058

(iv)

= 0.007

(v)

= 0.0048

(vi)

= 0.0003

Q.3. Divide:

(i) 235.41 by 1000

(ii) 29.5 by 1000

(iii) 3.8 by 1000

(iv) 0.7 by 1000

Ans: 

(i)

= 0.23451

(ii)

= 0.0295 

(iii)

= 0.0038 

(iv)

= 0.0007

Q.4. Divide:

(i) 0.45 by 9

(ii) 217.44 by 18

(iii) 319.2 by 2.28

(iv) 40.32 by 9.6

(v) 0.765 by 0.9

(vi) 0.768 by 1.6

Ans: 

(i)

=

= 0.05

(ii)

= 12.08

(iii)

= 140

(iv)

= 4.2

(v)

= 0.85 

(vi)

=

= 0.48

Q.5. Divide:

(i) 16.64 by 20

(ii) 0.192 by 12

(iii) 163.44 by 24

(iv) 403.2 by 96

(v) 16.344 by 12

(vi) 31.92 by 228

Ans: 

(i)

= 0.832

(ii)

= 0.016

(iii)

= 6.81

(iv)

= 4.2

(v)

=

= 1.362

(vi)

=

= 0.14

Q.6. Divide:

(i) 15.68 by 20

(ii) 164.6 by 200

(iii) 403.80 by 30

Ans: 

(i)

=

= 0.784 

(ii)

=

= 0.823 

(iii)

=

=

= 13.46

Q.7. Divide:

(i) 76 by 0.019

(ii) 88 by 0.08

(iii) 148 by 0.074

(iv) 7 by 0.014

Ans: 

(i)

= 4000

(ii)

= 1100 

(iii)

= 2000

(iv)

= 500

Q.8. Divide:

(i) 20 by 50

(ii) 8 by 100

(iii) 72 by 576

(iv) 144 by 15

Ans: 

(i)

=

= 0.4

(ii)

= 0.08 

(iii)

=

=

= 0.125

(iv)

=

= 9.6

Q.9. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it travel in 1 litre of petrol?

Ans: Distance travelled by the vehicle in 2.4 litres of petrol = 43.2 km

∴ Distance travelled in 1 litre of petrol will be:

=

= 18

Thus, the vehicle will travel 18 km in 1 litre of petrol.

Q.10. The total weight of some bags of wheat is 1743 kg. If each bag weights 49.8 kg, how many bags are there?

Ans: Let the number of bags of wheat be x.

Given:

Weight of x bags = 1,743 kg

Weight of one bag = 49.8 kg

Therefore, 49.8 × x = 1,743

x =

=

= 35

Thus, there are 35 bags of wheat.

Q.11. Shikha cuts 50 m of cloth into pieces of 1.25 m each. How many pieces does she get?

Ans: Length of cloth = 50 m

Length of one piece of cloth = 1.25 m

Let the number of pieces be x.

∴ Number of pieces of cloth × Length of each piece of cloth = Total length of cloth

x ×1.25 = 50

x =

=

= 40

Thus, she gets 40 pieces of 1.25 m cloth from a total of 50 m.

Q.12. Each side of a rectangular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have? 

Ans: Length of each side of the polygon  = 2.5 cm

Perimeter of the polygon = 12.5 cm

Let the number of sides of the polygon be z.

∴ 2.5 × z = 12.5 ( Perimeter = Length of one side multiplied by the number of sides)

or, z =

= 5 

Thus, the polygon has 5 sides.

Q.13. The product of two decimals is 42.987. If one of them is 12.46, find the other.

Ans: One decimal is 12.46.

Let the other decimal be x.

According to the question:

12.46 × x = 42.987

 x =

=

=

= 3.45

Thus, the other decimal is 3.45.

Q.14. The weight of 34 bags of sugar is 3483.3 kg. If all bags weigh equally, find the weight of each bag.

Ans: Number of bags = 34

Weight of 34 bags = 3483.3 kg

∴ Weight of one bag =

=

= 102.45

Thus, weight of each bag = 102.45 kg 

Q.15. How many buckets of equal capacity can be filled from 586.5 litres of water, if each bucket has capacity of 8.5 litres? 

Ans: Capacity of one bucket = 8.5 litres

Total water in all buckets = 586.5 litres

Let the number of buckets with equal capacity be x.

According to the question:

8.5 × x = 586.5

x =

=

= 69

Thus, there are 69 buckets.

Objective Type Questions

Q.1. Mark the correct alternative in each of the following:

When 0.48 is written in the simplest form of its terms, the sum of its numerator and denominator is

(a) 148                                         

(b) 74                                         

(c) 37                                         

(d) 147  

Ans:

=(HCF of 48 and 100=4)

=

Here,

Numerator = 12

Denominator = 25

∴ Sum of the numerator and denominator = 12 + 25 = 37

Hence, the correct answer is option (c).

Q.2. Mark the correct alternative in each of the following:

The improper fraction  in decimal form is

(a) 2.4                                        

(b) 2.04                                        

(c) 2.004                                         

(d) None of these

Ans: The given fraction is. Now,

=

=

=

= 2 + 0.04

= 2.04 

Hence, the correct answer is option (b).

Q.3. Mark the correct alternative in each of the following:

4 + 4.4 + 44.4 + 4.04 + 444 =

(a) 500.88                                         

(b) 577.2                                         

(c) 495.22                                         

(d) 472.88

Ans: Converting the decimals to like decimals, we have 4.00, 4.40, 44.40, 4.04 and 444.00.

Now,

∴ 4 + 4.4 + 44.4 + 4.04 + 444 = 500.84

Disclaimer: None of the options given in the question matches with the answer.

Q.4. Mark the correct alternative in each of the following:

1.04 as an improper fraction is

(a)                                       

(b)                                 

(c)                                

(d)

Ans: The given decimal is 1.04.

1.04

= 1 + 0.04

=

=

=

=

Hence, the correct answer is option (c).

Q.5. Mark the correct alternative in each of the following:

If 24.125 = 24 + , then A + B + C is

(a) 3                                         

(b) 6                                         

(c) 13                                         

(d) 8 

Ans: 

24.125 = 24 + 0.125 

= 24+0.1 + 0.02 + 0.005

=

Comparing this with the given expression, we get

A = 1, B = 2 and C = 5

∴ A + B + C = 1 + 2 + 5 = 8

Hence, the correct answer is option (d).

Q.6. Mark the correct alternative in each of the following:

0.002 × 0.5 =

(a) 0.0001                                         

(b) 0.001                                         

(c) 0.01                                        

(d) 1 

Ans: 0.002 × 0.5

=

=

=

=

= 0.001 

Hence, the correct answer is option (b).

Q.7. Mark the correct alternative in each of the following:

3 × 0.3 × 0.03 × 0.003 × 30 =  

(a) 0.0000243                     

(b) 0.000243                     

(c) 0.00243                     

(d) 0.243 

Ans: 3× 0.3 × 0.03 × 0.003 × 30

=

=

= 0.00243                  (Decimal point is shifted to left by 5 places)

Hence, the correct answer is option (c).

Q.8. Mark the correct alternative in each of the following:

0.012 × 0.15 =  

(a) 0.8                           

(b) 0.08                          

(c) 0.008                         

(d) 0.0018

Ans: We have,

12 × 15 = 180

It can be seen that the sum of the decimals in the given decimals is 3 + 2 = 5.

So, the product must contain 5 places of decimals.

∴ 0.012 × 0.15 = 0.00180 = 0.0018

Hence, the correct answer is option (d).

Q.9. Mark the correct alternative in each of the following:

75.57 ÷ 0.01 =

(a) 7557                                         

(b) 0.7557                                        

(c) 755.7                                         

(d) 7.557

Ans: 75.57 ÷ 0.01

=

=

(Multiply numerator and denominator by 100 to convert the divisor into whole number)

=

=7557

Hence, the correct answer is option (a).

Q.10. Mark the correct alternative in each of the following:

What should be subtracted from 0.1 to get 0.06?

(a) 0.4                                         

(b) 0.04                                        

(c) 0.004                                         

(d) None of these

Ans: The decimal which should be subtracted from 0.1 to get 0.06 can be obtained by subtracting 0.06 from 0.1.

Converting the given decimals into like decimals, we have 0.10 and 0.06.

Now,

∴ Required decimal = 0.1 − 0.06 = 0.04

Hence, the correct answer is option (b).

Q.11. Mark the correct alternative in each of the following:

What should be added to 5.09 to get 5.5?

(a) 0.41                                         

b) 0.59                                         

(c) 0.49                                         

(d) 0.95

Ans: The decimal number which should be added to 5.09 to get 5.5 is obtained by subtracting 5.09 from 5.5.

Converting the given decimals to like decimals, we have 5.09 and 5.50.

Now,

∴ Required decimal = 5.50 − 5.09 = 0.41

Thus, 0.41 must be added to 5.09 to get 5.5.

Hence, the correct answer is option (a).

Q.12. Mark the correct alternative in each of the following:

0.3 × 0.3 × 0.3 =

(a) 2.7                                         

(b) 0.27                                         

(c) 0.027                                         

(d) None of these

Ans: We have,

3 × 3 × 3 = 27

The sum of the decimal places in the given decimals is 1 + 1 + 1 = 3.

So, the product must contain 3 places of decimals.

∴ 0.3 × 0.3 × 0.3 = 0.027

Hence, the correct answer is (c).

Q.13. Mark the correct alternative in each of the following:

0.25 × 0.8 =

(a) 0.02                                        

(b) 0.2                                        

(c) 0.002                                         

(d) 2

Ans: In order to find the product, we first multiply 8 by 25.

We have, 25 × 8 = 200

Now, 0.25 has 2 decimal places and 0.8 has 1 decimal place.

The sum of the decimal places is 2 + 1 = 3.

So, the product must contain 3 places of decimals.

∴ 0.25 × 0.8 = 0.200 = 0.2

Hence, the correct answer is option (b).

Q.14. Mark the correct alternative in each of the following:

5 kg 5 g written in decimal notation is

(a) 5.5 kg                             

(b) 5.05 kg                             

(c) 5.005 kg                             

(d) 5.0005 kg

Disclaimer: The units are missing from the options given in the book.

Ans: We know that,

1 g =

Now,

5 kg 5 g = 5 kg + 5 g

=

= 5 kg + 0.005 kg

= 5.005 kg

∴ 5 kg 5 g = 5.005 kg

Hence, the correct answer is option (c).

Q.15. Mark the correct alternative in each of the following:

0.012 ÷ 1.5 = ?

(a) 0.8                                         

(b) 0.08                                         

(c) 0.008                                         

(d) None of these 

Ans: 0.012 ÷ 1.5

=

=

(Multiply the numerator and denominator by 10 to convert the divisor into a whole number)

=

∴ 0.012 ÷ 1.5 = 0.008

Hence, the correct answer is option (c).

Q.16. Mark the correct alternative in each of the following:

0.02 × 0.05 =

(a) 0.1                                        

(b) 0.01                                        

(c) 0.001                                         

(d) 0.0001

Ans: In order to find the product, we first multiply 2 by 5.

We have, 2 × 5 = 10

Now, 0.02 has 2 decimal places and 0.05 has 2 decimal places.

The sum of the decimal places is 2 + 2 = 4.

So, the product must contain 4 places of decimals.

∴ 0.02 × 0.05 = 0.0010 = 0.001

Hence, the correct answer is option (c).

Q.17. Mark the correct alternative in each of the following:

5 km 5 m = ?

(a) 5.5 km                        

(b) 5.05 km                         

(c) 5.005 km                         

(d) 5.0005 km

Ans: We know that,

1 m =

Now,

5 km 5 m = 5 km + 5 m

=

= 5 km + 0.005 km

= 5.005 km

∴ 5 km 5 m = 5.005 km

Hence, the correct answer is option (c).

Q.18. Mark the correct alternative in each of the following:

The value of 2.2 × 0.2 × 0.001 is

(a) 4.2                                         

(b) 0.00044                                        

(c) 4.4                                         

(d) None of these

Ans: In order to find the product, we first multiply 22 by 2.

We have, 22 × 2 = 44

Now, 2.2 has 1 decimal place, 0.2 has 1 decimal place and 0.001 has 3 decimal places.

The sum of the decimal places is 1 + 1 + 3 = 5.

So, the product must contain 5 places of decimals.

∴ 2.2 × 0.2 × 0.001 = 0.00044

Thus, the value of 2.2 × 0.2 × 0.001 is 0.00044.

Hence, the correct answer is option (b).

Q.19. Mark the correct alternative in each of the following:

If 14 × 4 = 56, then 0.014 × 4 =

(a) 0.56                                         

(b) 5.6                                         

(c) 0.056                                         

(d) None of these

Ans: It is given that,

14 × 4 = 56

Now, 0.014 has 3 decimal places.

So, the required product must contain 3 places of decimals.

∴ 0.014 × 4 = 0.056

Hence, the correct answer is option (c).

Q.20. Mark the correct alternative in each of the following:

8 ml is equal to

(a) 0.8 l                                         

(b) 0.08 l                                         

(c) 0.008 l                                         

(d) None of these

Ans: We know that,

1 mL =

∴ 8 mL =

Hence, the correct answer is option (c).