The DAV Class 7 Maths Book Solutions Pdf and **DAV Class 7 Maths Chapter 3 Worksheet 3** Solutions of Rational Numbers as Decimals offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 3 WS 3 Solutions

Question 1.

Express the following decimals as rational numbers in standard form.

(i) 0.25

Answer:

0.25 = \(\frac{25}{100}=\frac{25 \div 25}{100 \div 25}\)

= \(\frac{1}{4}\)

(ii) -0.052

Answer:

-0.052 = \(\frac{-52}{1000}=\frac{-52 \div 4}{1000 \div 4}\)

= \(\frac{-13}{250}\)

(iii) 7.50

Answer:

7.50 = \(\frac{750}{100}=\frac{750 \div 50}{100 \div 50}\)

= \(\frac{15}{2}\)

(iv) – 2.15

Answer:

-2.15 = \(\frac{-215}{100}=\frac{-215 \div 5}{100 \div 5}\)

= \(\frac{-43}{20}\)

(v) 0.036

Answer:

0.036 = \(\frac{36}{1000}=\frac{36 \div 4}{1000 \div 4}\)

= \(\frac{9}{250}\)

(vi) -9.6

Answer:

-9.6 = \(\frac{-96}{10}=\frac{-96 \div 2}{10 \div 2}\)

= \(\frac{-48}{5}\)

(vii) 31.25

Answer:

31.25 = \(\frac{3125}{100}=\frac{3125 \div 25}{100 \div 25}\)

= \(\frac{125}{4}\)

(viii) 16.32

Answer:

16.32 = \(\frac{1632}{100}=\frac{1632 \div 4}{100 \div 4}\)

= \(\frac{408}{25}\)

(ix) 0.107

Answer:

0.107 = \(\frac{107}{1000}\) (standard form)

Question 2.

Add the following decimals.

(i) 2.5, 7.51 and 11.501

Answer:

2.5 + 7.51 + 11.501

= 2.500 + 7.510 + 11.501

= 21.511

OR

(ii) 12, 5.96 and 3.076

Answer:

12 + 5.96 + 3.076

= 12.000 + 5.960 + 3.076

= 21.036

OR

(iii) 9.08, 19.76 and 20.54

Answer:

9.08 + 19.76 + 20.54

= 49.38

OR

(iv) 3.009, 0.592 and 14.745

Answer:

3.009 + 0.592 + 14.745

= 18.346

OR

(v) 19, 9.5, 12.06 and 17.921

Answer:

19 + 9.5 + 12.06 + 17.921

= 19.000 + 9.500 + 12.060 + 17.921

= 58.481

OR

Question 3.

Compute the following products of decimals.

(i) 2.9 × 3.5

Answer:

2.9 × 3.5 = 29 × 35

Now putting the decimal in the result, we get 10.15

(ii) 37 × 12.76

Answer:

37 × 12.76 = 1276 × 37

Now putting the decimal in the result, we get 472.12

(iii) 0.84 × 8.8

Answer:

(iii) 0.84 × 8.8 = 84 × 88 84

Now putting the decimal in the result, we get 7.392

(iv) 2.56 × 11.09

Answer:

2.56 × 11.09 = 256 × 1109

Putting the decimal in the result, we get 28.3904

(v) 12.4 × 15.7 × 13.2

Answer:

12.4 × 15.7 = 124 × 157

Puttting the decimal = 1569.776

Question 4.

(i) 59.049 ÷ 9

Answer:

(ii) 6.4 ÷ 0.2

Answer:

(iii) 0.015 ÷ 3

Answer:

= 0.005

(iv) 0.014 ÷ 12

Answer:

(v) 0.02472 ÷ 0.008

Answer:

(vi) 51.51 ÷ 0.17

Answer:

Question 5.

Evaluate the following:

(i) 25.75 + 2.09 – 13.6

Answer:

25.75 + 2.09 – 13.6

= (25.75 + 2.09) – 13.60

= 27.84 – 13.60

= 14.24

(ii) 37 -16.58 + 12.25

Answer:

37-16.58 + 12.25

= 37.00 – 16.58 + 12.25

= (37.00 + 12.25) – 16.58

= 49.25 – 16.58

= 32.67

(iii) 42.7 – 11 – 9.025 + 2.16

Answer:

42.7 – 11 – 9.025 + 2.16

= 42.700 – 11.000 – 9.025 + 2.160

= (42.700 + 2.160) – (11.000 + 9.025)

= 44.860 – 20.025

= 24.835

(iv) (6.05 + 5.01) – (12.5 – 0.09)

Answer:

(6.05 + 5.01) – (12.5 – 0.09)

= (6.05 + 5.01) – (12.50 – 0.09)

= 11.06 – 12.41

= -0.35

(v) 182.3 + 12.65 – 0.23 -10.71

Answer:

182.3 + 12.65 – 0.23 – 10.71

= 182.30 + 12.65 – 0.23 – 10.71

= (182.30 – 0.23) + (12.65 – 10.71)

= 182.07 + 1.94

= 184.01

Question 6.

Simplify and express the result as a rational number in its lowest terms.

(i) \(\frac{1}{2}+\frac{1}{5}\) + 6.25 ÷ 0.25

Answer:

(ii) \(\frac{2}{5}-\frac{1}{4}\) + (8.1 × 2.7) ÷ 0.09

Answer:

(iii) 1.44 × (144 ÷ 12) – 0.225 + 3.276

Answer:

= 1.44 × \(\frac{144}{12}\) – 0.225 + 3.276

= 1.44 × 12 – 0.225 + 3.276

= 17.28 + (3.276 – 0.225)

= 17.28 + 3.051

= 17.280 + 3.051 = 20.331

= \(\frac{20331}{1000}\)

(iv) \(\frac{1}{7}\) × 0.049 + \(\frac{3}{8}-\frac{7}{20}\)

Answer:

(v) 5 × 0.16 – 0.52 + 8.263

Answer:

5 × 0.16 – 0.52 + 8.263

= 0.80 – 0.52 + 8.263

= 0.800 – 0.520 + 8.263

= (0.800 + 8.263) – 0.520

= 9.063 – 0.520

= 8.543

(vi) \(\frac{2}{5} \times \frac{3}{4}+\frac{1}{25} \times \frac{1}{2}-\frac{2}{10} \times \frac{1}{5}\)

Answer:

### DAV Class 7 Maths Chapter 1 Value Based Questions

Question 1.

Megha bought a book for ₹ 112\(\frac{1}{2}\) from a shop. She gave 500 rupee note to shopkeeper and go the balance back. But, she realised that the shopkeeper had given her ₹ 72 extra. Megha returned the extra money and had a feeling of great satisfaction.

(i) How much money had the shopkeeper returned to Megha?

Answer:

Price of book = ₹ 112\(\frac{1}{2}\)

= ₹ \(\frac{225}{2}\)

= ₹ 112.5

Money that was given by Megha to shopkeeper = ₹ 500

∴ Balance = ₹ 500 – ₹ 112.5

= ₹ 387.5

Now, money that had been returned to megha by the shopkeeper = ₹ 387.5 + ₹ 72

= ₹ 459.5

= ₹ 459

(ii) What values did Megha exhibit in the above situation?

Answer:

Values: Megha is a honest girl. She showed honesty by returning th extra money to the shopkeeper.

Question 2.

Raman had to cover a distance of 30 km to reach his grandmother’s house. He covered 11.25 km by bus, 7.083 km by auto and rest by foot.

(i) How much distance did Roman cover by foot?

Answer:

Total distance to be covered = 30 km

Distance covered by bus = 11.25 km

Distance covered by auto = 7.083 km

Distance covered by foot = Total distance – (distance covered by bus + distance covered by auto)

Distance covered by foot = 30 km – (11.25 km + 7.08 km)

= 30 km 18.33 km

= 11.67 km

Therefore, Raman covered distance of 11.67 km by foot.

(ii) How is Raman benefitted if he walks down to any of his destination? In what ways it effect our environment?

Answer:

Walking keeps him healthy and physically fit.

Environment remains pollution free.