Chapter 2 Fractions and Decimals Exercise 2.5
Question 1: Which is greater?
(i) 0.5 or 0.05
Answer:
0.5 = 5/10
0.05 = 5/100
LCM of 10, 100 = 100
= 5/10 × 10/10 = 50/100
= 5/100 × 1/1 = 5/100
Comparing 50/100 [] 5/100
50/100 > 5/100
Therefore, 0.5 is greater.
(ii) 0.7 or 0.5
Answer:
0.7 = 7/10
0.5 = 5/10
Comparing 7/10 [] 5/10
70/10 > 5/10
Therefore, 0.7 is greater.
(iii) 7 or 0.7
Answer:
0.5 = 7/1
0.7 = 7/10
LCM of 1, 10 = 10
= 7/1 × 10/10 = 70/10
= 7/10 × 1/1 = 7/10
Comparing 70/10 [] 7/10
70/10 > 7/10
Therefore, 7 is greater.
(iv) 1.37 or 1.49
Answer:
1.37 = 137/100
1.49 = 149/100
LCM of 100, 100 = 100
= 137/100 × 1/1 = 137/100
= 149/100 × 1/1 = 149/100
Comparing 137/100 [] 149/100
137/100 < 149/100
Therefore, 1.49 is greater.
(v) 2.03 or 2.30
Answer:
2.03 = 203/100
2.30 = 230/100
LCM of 100, 100 = 100
= 203/100 × 1/1 = 203/100
= 230/100 × 1/1 = 230/100
Comparing 203/100 [] 230/100
203/100 < 230/100
Therefore, 2.30 is greater.
(vi) 0.8 or 0.88
Answer:
0.8 = 8/10
0.88 = 88/100
LCM of 10, 100 = 100
= 8/10 × 10/10 = 80/100
= 88/100 × 1/1 = 88/100
Comparing 80/100 [] 88/100
80/100 < 88/100
Therefore, 0.88 is greater.
Question 2: Express as rupees as decimals:
(i) 7 paise
Answer:
= ₹ 1 = 100 paise
= 1 paise = ₹ 1/100
7 paise = ₹ 7/100
= ₹ 0.07
(ii) 7 rupees 7 paise
Answer:
= ₹ 1 = 100 paise
= 1 paise = ₹ 1/100
7 rupees 7 paise = ₹ 7 + ₹ 7/100
= ₹ 7 + ₹ 0.07
= ₹ 7.07
(iii) 77 rupees 77 paise
Answer:
= ₹ 1 = 100 paise
= 1 paise = ₹ 1/100
77 rupees 77 paise = ₹ 77 + ₹ 77/100
= ₹ 77 + ₹ 0.77
= ₹ 77.77
(iv) 50 paise
Answer:
= ₹ 1 = 100 paise
= 1 paise = ₹ 1/100
50 paise = ₹ 50/100
= ₹ 0.50
(v) 235 paise
Answer:
= ₹ 1 = 100 paise
= 1 paise = ₹ 1/100
235 paise = ₹ 235/100
= ₹ 2.35
Question 3: (i) Express 5 cm in meter and kilometer
Answer:
= 1 meter = 100 cm
= 1 cm = 1/100 m
= 5 cm = 5/100
= 0.05 m
Therefore, 5 cm is equal to 0.05 m.
= 1 km = 1000 m
= 1 m = 1/1000 km
= 0.05 m = 0.05/1000
= 0.00005 km
Therefore, 5 cm is equal to 0.00005 km.
(ii) Express 35 mm in cm, m and km
Answer:
= 1 cm = 10 mm
= 1 mm = 1/10 cm
= 35 mm = 35/10 cm
= 3.5 cm
Therefore, 35 mm is equal to 3.5 cm.
= 1 meter = 100 cm
= 1 cm = 1/100 m
= 3.5 cm = 3.5/100 m
= 35/1000 m
= 0.035 m
Therefore, 35 mm is equal to 0.035 m.
= 1 km = 1000 m
= 1 m = 1/1000 km
= 0.035 m = 0.035/1000
= 0. 000035 km
Therefore, 35 mm is equal to 0. 000035 km.
Question 4: Express in kg:
(i) 200 g
Answer:
= 1 kg = 1000 g
= 1 g = 1/1000 kg
= 200 g = 200/1000 kg
= 2/10
= 0.2 kg
(ii) 3470 g
Answer:
= 1 kg = 1000 g
= 1 g = 1/1000 kg
= 3470 g = 3470/1000 kg
= 347/100
= 3.47 kg
(iii) 4 kg 8 g
Answer:
= 1 kg = 1000 g
= 1 g = 1/1000 kg
= 4 kg 8 g = 4 kg + 8/1000 kg
= 4 kg + 0.008
= 4.008 kg
Question 5: Write the following decimal numbers in the expanded form:
(i) 20.03
Answer: 20.03 = (2 × 10) + (0 × 1) + (0 × 1/10) + (3 × 1/100)
(ii) 2.03
Answer: 2.03 = (2 × 1) + (0 × 1/10) + (3 × 1/100)
(iii) 200.03
Answer: 200.03 = (2 × 100) + (0 × 10) + (0 × 1) + (0 × 1/10) + (3 × 1/100)
(iv) 2.034
Answer: 2.034 = (2 × 1) + (0 × 1/10) + (3 × 1/100) + (4 × 1/1000)
Question 6: Write the place value of 2 in the following decimal numbers:
(i) 2.56
Answer: The place value of 2 in 2.56 is ones.
(ii) 21.37
Answer: The place value of 2 in 21.37 is tens.
(iii) 10.25
Answer: The place value of 2 in 10.25 is tenths.
(iv) 9.42
Answer: The place value of 2 in 9.42 is hundredth.
(v) 63.352
Answer: The place value of 2 in 63.352 is thousandth.
Question 7: Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?
Distance between A and B = 7.5 km
Distance between B and C = 12.7 km
Distance between D and A = 11.8 km
Distance between C and D = 11.8 km
Distance travelled by Dinesh = AB + BC
= 7.5 + 12.7
= 20.2 km
Therefore, Dinesh travelled 20.2 km.
Distance travelled by Ayub = AD + DC
= 9.3 + 11.8
= 21.1 km
Therefore, Ayub travelled 21.1 km.
Comparing 20.2 km [] 21.1 km
= 20.2 km < 21.1 km
Therefore, Ayub travelled more distance.
= 21.1 km - 20.2 km
= 0.9 km
Therefore, Ayub travelled 0.9 km more than Dinesh.
Question 8: Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
Answer:
Shyama
Weight of Apples brought = 5 kg 300 g
Weight of Mangoes brought = 3 kg 250 g
Total weight brought by him = ?
= 5 kg 300 g + 3 kg 250 g = 8 kg 550 g
Sarala
Weight of Oranges brought = 4 kg 800 g
Weight of Bananas brought = 4 kg 150 g
Total weight brought by him = ?
= 4 kg 800 g + 4 kg 150 g = 8 kg 950 g
Comparing 8 kg 550 g (Shyama) [] 8 kg 950 g (Sarala)
= 8 kg 550 g (Shyama) < 8 kg 950 g (Sarala)
Therefore, Sarala bought more fruits.
Question 9: How much less is 28 km than 42.6 km?
Answer:
= 42.6 km - 28 km
= 14.6
Therefore, 14.6 km less is 28 km than 42.6 km.
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