RD Sharma solution class 7 chapter 3 Decimals Exercise Objective Type Questions

Objective Type Questions 

Page-3.18

Question 4:

Mark the correct alternative in each of the following:

1.04 as an improper fraction is

(a) $1\frac{1}{5}$                                         (b) $1\frac{2}{5}$                                         (c) $1\frac{1}{25}$                                         (d) $1\frac{2}{25}$                                        

Answer 4:

The given decimal is 1.04.

$$\begin{gathered} 1.04 \\ =1+0.04 \\ =1+\frac{4}{100} \\ =1+\frac{4÷4}{100÷4} \\ =1+\frac{1}{25} \\ =1\frac{1}{25} \end{gathered}$$

Hence, the correct answer is option (c).

Question 5:

Mark the correct alternative in each of the following:

If $24.125=24+\frac{A}{10}+\frac{B}{100}+\frac{C}{1000}$, then A + B + C is

(a) 3                                         (b) 6                                         (c) 13                                         (d) 8                                        

Answer 5:

$$\begin{gathered} 24.125 \\ =24+0.125 \\ =24+0.1+0.02+0.005 \\ =24+\frac{1}{10}+\frac{2}{100}+\frac{5}{1000} \end{gathered}$$

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).

Question 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                                                                 

Answer 6:

$$\begin{gathered} 0.002\times 0.5 \\ =\frac{2}{1000}\times \frac{5}{10} \\ =\frac{2\times 5}{1000\times 10} \\ =\frac{10}{10000} \\ =\frac{1}{1000} \\ =0.001 \end{gathered}$$

Hence, the correct answer is option (b).

Question 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                                   

Answer 7:

$$\begin{gathered} 3\times 0.3\times 0.03\times 0.003\times 30 \\ =3\times \frac{3}{10}\times \frac{3}{100}\times \frac{3}{1000}\times 3\times 10 \\ =\frac{3\times 3\times 3\times 3\times 3}{100\times 1000} \\ =\frac{243}{100000} \\ =0.00243 \left(\mathrm{Decimal} \mathrm{point} \mathrm{is} \mathrm{shifted} \mathrm{to} \mathrm{left} \mathrm{by} 5 \mathrm{places}\right) \end{gathered}$$

Hence, the correct answer is option (c).

Question 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

Answer 8:

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).

Question 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                                       

Answer 9:

$$\begin{gathered} 75.57÷0.01 \\ =\frac{75.57}{0.01} \\ =\frac{75.57\times 100}{0.01\times 100} \left(\mathrm{Multiply} \mathrm{numerator} \mathrm{and} \mathrm{denominator} \mathrm{by} 100 \mathrm{to} \mathrm{convert} \mathrm{the} \mathrm{divisor} \mathrm{into} \mathrm{whole} \mathrm{number}\right) \\ =\frac{7557}{1} \\ =7557 \end{gathered}$$

Hence, the correct answer is option (a).

Question 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                                       

Answer 10:

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,

$\begin{array}{ccccc}& 0& .& 1& 0\\ -& 0& .& 0& 6\\ & 0& .& 0& 4\end{array}$

∴ Required decimal = 0.1 − 0.06 = 0.04

Hence, the correct answer is option (b).

Question 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                                       

Answer 11:

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,

$\begin{array}{ccccc}& 5& .& 5& 0\\ -& 5& .& 0& 9\\ & 0& .& 4& 1\end{array}$

∴ 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).

Question 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                                       

Answer 12:

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).

Question 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                                     

Answer 13:

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).

Question 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.                                      

Answer 14:

We know that,

1 g = $\frac{1}{1000}$ kg

Now,

5 kg 5 g = 5 kg + 5 g

              = 5 kg + $\frac{5}{1000}$ kg

              = 5 kg + 0.005 kg

              = 5.005 kg

∴ 5 kg 5 g = 5.005 kg

Hence, the correct answer is option (c).

Question 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                                       

Answer 15:

$$\begin{gathered} 0.012÷1.5 \\ =\frac{0.012}{1.5} \\ =\frac{0.012\times 10}{1.5\times 10} \left(\mathrm{Multiply} \mathrm{the} \mathrm{numerator} \mathrm{and} \mathrm{denominator} \mathrm{by} 10 \mathrm{to} \mathrm{convert} \mathrm{the} \mathrm{divisor} \mathrm{into} \mathrm{a} \mathrm{whole} \mathrm{number}\right) \\ =\frac{0.12}{15} \end{gathered}$$


∴ 0.012 ÷ 1.5 = 0.008

Hence, the correct answer is option (c).

Question 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                                       

Answer 16:

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).

Question 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

Answer 17:

We know that,

1 m = $\frac{1}{1000}$ km

Now,

5 km 5 m = 5 km + 5 m

              = 5 km + $\frac{5}{1000}$ km

              = 5 km + 0.005 km

              = 5.005 km

∴ 5 km 5 m = 5.005 km

Hence, the correct answer is option (c).

Question 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                                       

Answer 18:

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).

Question 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                                       

Answer 19:

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).

Question 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                                      

Answer 20:

We know that,

1 mL = $\frac{1}{1000}$ L

∴ 8 mL = $\frac{8}{1000}$ L = 0.008 L

Hence, the correct answer is option (c).