Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 8 Decimals Ex 8.4 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 6 Maths Chapter 8 Decimals Ex 8.4
Question 1.
Express as rupees using decimals.
(a) 5 paise
(b) 75 paise
(c) 20 paise
(d) 50 rupees 90 paise
(e) 725 paise
Solution:
(a) 5 paise
∵ 1 paisa = ₹ \(\frac { 1 }{ 100 }\)
∴ 5 paise = ₹ 5 × \(\frac { 1 }{ 100 }\) = ₹ \(\frac { 5 }{ 100 }\) = ₹ 0.05
(b) 75 paise
∵ 1 paisa = ₹ \(\frac { 1 }{ 100 }\)
75 paise = ₹ 75 × \(\frac { 1 }{ 100 }\) = ₹ \(\frac { 75 }{ 100 }\) = ₹ 0.75
(c) 20 paise
∵ 1 paisa = ₹ \(\frac { 1 }{ 100 }\)
∴ 20 paise = ₹ 20 × \(\frac { 1 }{ 100 }\) = ₹ \(\frac { 20 }{ 100 }\) = ₹ 0.20
(d) 50 rupees 90 paise
∵ 1 paisa = ₹ \(\frac { 1 }{ 100 }\)
∴ 90 paise = ₹ 90 × \(\frac { 1 }{ 100 }\) = ₹ 0.90
Now, 50 rupees + 90 paise
= ₹ 50 + ₹ 0.90 = ₹ (50 + 0.90) = ₹ 50.90
(e) 725 paise
∵ 1 paisa = ₹ \(\frac { 1 }{ 100 }\)
∴ 725 paise = ₹ 725 × \(\frac { 1 }{ 100 }\) = ₹ \(\frac { 725 }{ 100 }\)
= ₹ [7 + 0.25] = ₹ 7.25
Question 2.
Express as km using decimals.
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
(e) 419 cm
Solution:
(a) 15 cm
∵ 100 cm = 1 m
∴ 1 cm = \(\frac { 1 }{ 100 }\) m
So 15 cm = 15 × \(\frac { 1 }{ 100 }\)m = \(\frac { 15 }{ 100 }\)m = 0.15 m
(b) 6 cm
∵ 1 cm = \(\frac { 1 }{ 100 }\) m
∴ 6 cm = \(\frac { 1 }{ 100 }\) m = \(\frac { 6 }{ 100 }\)m = 0.06 m
(c) 2 m 45 cm
∵ 1 cm = \(\frac { 1 }{ 100 }\) m
∴ 2 m 45 cm = 2 m + 45 cm
2 m 45 cm = 2 m + 45 × \(\frac { 1 }{ 100 }\) m
= 2 m + 0.45 m
= (2 + 0.45) m = 2.45 m
(d) 9 m 7 cm
∵ 1 cm = \(\frac { 1 }{ 100 }\) m
∴ 9 m 7 cm = 9 m + 7 cm
9 m + 7 cm = 9 m + 7 × \(\frac { 1 }{ 100 }\) m
= 9 m + 0.07 m
9 m 7 cm = (9 + 0.07)m = 9.07 m
(e) 419 cm
∵ 1 cm = \(\frac { 1 }{ 100 }\) m
∴ 419 cm = 419 × \(\frac { 1 }{ 100 }\) m = \(\frac { 419 }{ 100 }\) m
= \(\left(\frac{400}{100}+\frac{19}{100}\right)\) m = \(\left(4+\frac{19}{100}\right)\) m
= (4 + 0.19) m = 4.19 m
Question 3.
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm
Solution:
(a) 5 mm
∵ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 5 mm = 5 × \(\frac { 1 }{ 10 }\) cm = \(\frac { 5 }{ 10 }\) cm = 0.5 cm
(b) 60 mm
∵ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 60 mm = 60 × \(\frac { 1 }{ 10 }\) cm = \(\frac { 60 }{ 10 }\) cm = 6.0 cm
(c) 164 mm
∵ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 164 mm = 164 × \(\frac { 1 }{ 10 }\) cm = \(\frac { 164 }{ 10 }\) cm
= \(\left(\frac{100+60+4}{10}\right)\) cm = \(\left(\frac{100}{10}+\frac{60}{10}+\frac{4}{10}\right)\) cm
= \(\left(10+6+\frac{4}{10}\right)\) cm = 16.4 cm
(d) 9 cm 8 mm
∵ 1 mm = \(\frac { 1 }{ 10 }\) cm and 9 cm 8 mm = 9 cm 8 mm
∴ 9 cm 8 mm = 9 cm + 8 × \(\frac { 1 }{ 10 }\) cm
= 9 cm + 0.8 cm
= (9 + 0.8) cm = 9.8 cm
(e) 93 mm
∵ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 93 mm = 93 × \(\frac { 1 }{ 10 }\) cm
= \(\frac { 93 }{ 10 }\) cm = \(\left(\frac{90}{10}+\frac{3}{10}\right)\) cm
= (9 + 0.3) cm = 9.3 cm
Question 4.
Express as km using decimals.
(a) 8 m
(b) 88 m
(c) 8888 m
(d) 70 km 5 m
Solution:
(a) 8 m
∵ 1000 m = 1 m
∴ 1 m = \(\frac { 1 }{ 1000 }\) km
Now, 8 m = 8 × \(\frac { 1 }{ 1000 }\) km
= \(\frac { 8 }{ 1000 }\) km = 0.008 km
(b) 88 m
∵ 1000 m = 1 m
∴ 1 m = \(\frac { 1 }{ 1000 }\) km
Now, 8 m = 88 × \(\frac { 1 }{ 1000 }\) km
= \(\frac { 88 }{ 1000 }\) km = 0.088 km
(c) 8888 m
∵ 1 m = \(\frac { 1 }{ 1000 }\) km
∴ 8888 m = 8888 × \(\frac { 1 }{ 1000 }\) km = \(\frac { 8888 }{ 1000 }\) km
= \(\left[\frac{8000+888}{1000}\right]\) km = \(\left[\frac{8000}{1000}+\frac{888}{1000}\right]\) km
= [8 + 0.888] km = 8.888 km
(d) 70 km 5 m
∵ 1 m = \(\frac { 1 }{ 1000 }\) km and 70 km 5 m = 70 km + 5 m
∴ 70 km 5 m = 70 km + 5 × \(\frac { 1 }{ 1000 }\) km
= \(\left[70+\frac{5}{1000}\right]\) km
= [70 + 0.005] km = 70.005 km
Question 5.
Express as kg using decimals.
(a) 2 g
(b) 100 g
(c) 3750 g
(d) 5 kg 8 g
(e) 26 kg 50 g
Solution:
(a) 2 g
∵ 1000 g = 1 kg
∴ 1 g = \(\frac { 1 }{ 1000 }\) kg
Now 2 g = 2 × \(\frac { 1 }{ 1000 }\) kg
= \(\frac { 2 }{ 1000 }\) kg = 0.002 kg
(b) 100 g
∵ 1 g = \(\frac { 1 }{ 1000 }\) kg
∴ 100 g = \(\frac { 1 }{ 1000 }\) kg
= \(\frac { 1 }{ 1000 }\) kg × 100 kg = 0.1 kg
(c) 3750 g
∵ 1 g = \(\frac { 1 }{ 1000 }\) kg
∴ 3750 g = 3750 × \(\frac { 1 }{ 1000 }\) kg
= \(\frac { 3750 }{ 1000 }\) kg
= \(\left(\frac{3000+750}{1000}\right)\) kg = \(\left(\frac{3000}{1000}+\frac{750}{1000}\right)\) kg
= (3 + 0.750) kg = 3.750 kg
(d) 5 kg 8 g
∵ 1 g = \(\frac { 1 }{ 1000 }\) kg and 5 kg 8 g = 5 kg + 8 g
∴ 5 kg 8 g = 5 kg + 8 × \(\frac { 1 }{ 1000 }\) kg
= \(\left(5+\frac{8}{1000}\right)\) kg
= (5 + 0.008) kg = 5.008 kg
(e) 26 kg 50 g
∵ 1 g = \(\frac { 1 }{ 1000 }\) kg and 26 kg 50 g = 26 kg + 50 g
∴ 26 kg 50 g = 26 kg + 50 × \(\frac { 1 }{ 1000 }\) kg
= 26 kg + \(\frac { 50 }{ 1000 }\) kg = \(\left(26+\frac{50}{1000}\right)\) kg
= (26 + 0.050) kg = 26.050 kg