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.