## NCERT Solutions Class 6 Maths Chapter - 8: Decimals## Exercise 8.1
(a)
Total number of Hundreds = 0 Total number of tens = 3 Total number of ones = 1 Total number of tenths = 2 0 Hundreds + 3 tens + 1 ones + 2 tenths = 0 × 100 + 3 × 10 + 1 × 1 + 2 × 1/10 = 0 + 30 + 1 + 0.2 = 31.2 (b)
Total number of Hundreds = 1 Total number of tens = 1 Total number of ones = 0 Total number of tenths = 4 1 Hundreds + 1 tens + 0 ones + 4 tenths = 1 × 100 + 1 × 10 + 0 × 1 + 4 × 1/10 = 100 + 10 + 0 + 0.4 = 110.4
- 19.4
- 0.3
- 10.6
- 205.9
19. 4 = 10 + 9 + 0.4 = 1 × 10 + 9 × 1 + 4 × 1/10 = 1 × Tens + 9 × Ones + 4 × Tenths Since there are no hundreds, so hundred = 0.
0.3 = 3 × 1/10 = 3 × Tenths
10.6 = 10 + 0.6 = 1 × 10 + 6 × 1/10 = 1 × Tens + 6 × Tenths Since there are no hundreds and ones, so hundred = 0, Ones = 0.
205.9 = 200 + 5 + 0.9 = 2 × 100 + 5 × 1 + 9 × 1/10 = 2 × Hundreds + 5 × Ones + 9 × Tenths Since there are no tens and ones, so tens = 0.
= 0.7
= 14 + 0.6 = 14.6
= 1 × 100 + 2 × 1 = 100 + 2 = 102 Since there are no tenths, so place after decimal will be 0
= 600 + 0.8 = 600.8
= 5 tenths = 0.5
= 3 × 1 + 7 × 1/10 = 3 + 0.7 = 3.7
= 2 × 100 + 6 × 10 + 5 × 1 + 1 × 1/10 = 200 + 60 + 5 + 0.1 265.1
= 7 × 10 + 8 × 1/10 = 70 + 0.8 = 70.8
= 8.8
= 4.2
(3 × 5)/ (2 × 5) = 15/10 = 15 tenths = 15 × 1/10 = 1.5
(2 × 2)/ (5 × 2) = 4/10 = 4 × 1/10 = 0.4
(12 × 2)/ (5 × 2) = 24/10 = 24 × 1/10 = 2.4
Let's multiply the fraction (3/5) by 2, 3 + (3 × 2)/ (5 × 2) = 3 + 6/10 = 3 + 0.6 = 3.6
Let's multiply the fraction (1/2) by 5, = 4 + (1 × 5)/ (2 × 5) = 4 + 5/10 = 4 + 0.5 = 4.5
Both 6 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form. (2 × 3)/ (2 × 5) = 3/5
2.5 = 25/10 Both 25 and 10 have a common factor 5. Let's divide the numerator and the denominator by 5 to convert the fraction to its lowest form. (5 × 5)/ (2 × 5) = 5/2
= 10/10 = 1
= 38/10 Both 38 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form. (2 × 19 (2 × 5) = 19/5
The numerator and the denominator do not have any factor in common. It is already present in its lowest form.
= 212/10 Both 212 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form. (2 × 106)/ (2 × 5) = 106/5
6.4 = 64/10 Both 64 and 10 have a common factor 2. Let's divide the numerator and the denominator by 2 to convert the fraction to its lowest form. (2 × 32)/ (2 × 5) = 32/5
1m = 100 cm 1 cm = 1/100 m 1 cm = 0.01 m 1 cm = 10 mm 1mm = 1/10 cm 1 mm = 0.1 cm
2 mm = 2 × 1/10 cm = 0.2 cm
30 mm = 30 × 1/10 cm = 30/10 cm = 3.0 cm
116 mm = 116 × 1/10 cm = 116/10 cm = 11.6 cm
4 cm + 2 × 1/10 cm = 4 + 0.2 = 4.2 cm
162 mm = 162 × 1/10 cm = 16.2 cm
83 mm = 83 × 1/10 cm = 83/10 cm = 8.3 cm
0.8 is nearer to the number 1.
The number 5.1 is nearer to the number 5.
The number 2.6 is nearer to the number 3.
The number 6.4 is nearer to the number 6.
The number 9.1 is nearer to the number 9.
The number 4.9 is nearer to the number 5.
(a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5
A = 0.8 B = 1.3 C = 2.2 D = 2.9
9 cm 5 mm = 9 cm + 5 × 1/10 cm = 9 cm + 5/10 cm = (9 + 0.5) cm = 9.5 cm
65 mm = 65 × 1/10 cm = 65/10 cm = 6.5 cm ## Exercise 8.2
(a) 0 Ones + 2 Tenths + 6 Hundredths = 0 × 1 + 2 × 1/10 + 6 × 1/100 = 0 + 2/10 + 6/100 = 0 + 0.2 + 0.06 = 0.26 (b) 1 Ones + 3 Tenths + 8 Hundredths = 1 × 1 + 3 × 1/10 + 8 × 1/100 = 1 + 3/10 + 8/100 = 1 + 0.3 + 0.08 = 1.38 (c) 1 Ones + 2 Tenths + 8 Hundredths = 1 × 1 + 2 × 1/10 + 8 × 1/100 = 1 + 2/10 + 8/100 = 1 + 0.2 + 0.08 = 1.28
(a)
0 Hundreds + 0 Tens + 3 Ones + 2 Tenths + 5 Hundredths + 0 Thousandths = 0 × 100 + 0 × 10 + 3 × 1 + 2 × 1/10 + 5 × 1/100 + 0 × 1/1000 = 0 + 0 + 3 + 2/10 + 5/100 + 0 = 3 + 0.2 + 0.05 = 3.25 (b)
1 Hundreds + 0 Tens + 2 Ones + 6 Tenths + 3 Hundredths + 0 Thousandths = 1 × 100 + 0 × 10 + 2 × 1 + 6 × 1/10 + 3 × 1/100 + 0 × 1/1000 = 100 + 0 + 2 + 6/10 + 3/100 + 0 = 100 + 2 + 0.6 + 0.03 = 102.63 (c)
0 Hundreds + 3 Tens + 0 Ones + 0 Tenths + 2 Hundredths + 5 Thousandths = 0 × 100 + 3 × 10 + 0 × 1 + 0 × 1/10 + 2 × 1/100 + 5 × 1/1000 = 0 + 30 + 0 + 0 + 2/100 + 5/1000 = 30 + 0.02 + 0.005 = 30.025 (d)
2 Hundreds + 1 Tens + 1 Ones + 9 Tenths + 0 Hundredths + 2 Thousandths = 2 × 100 + 1 × 10 + 1 × 1 + 9 × 1/10 + 0 × 1/100 + 2 × 1/1000 = 200 + 10 + 1 + 9/10 + 0 + 2/1000 = 211 + 0.9 + 0.002 = 211.902 (e)
0 Hundreds + 1 Tens + 2 Ones + 2 Tenths + 4 Hundredths + 1 Thousandths = 0 × 100 + 1 × 10 + 2 × 1 + 2 × 1/10 + 4 × 1/100 + 1 × 1/1000 = 0 + 10 + 2 + 2/10 + 4/100 + 1/1000 = 12 + 0.2 + 0.04 + 0.001 = 12.241
- 0.29
- 2.08
- 19.60
- 148.32
- 200.812
20 + 9 + 4/10 + 1/100 = 20 + 9 + 0.4 + 0.01 = 29.41
137 + 0.05 = 137.05
0.7 + 0.06 + 0.004 = 0.764
23.206
= 725.09
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10.07
(e) 0.032
(f) 5.008
(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57
Lowest refers to the value of a fraction where the numerator and the denominator has only 1 as the common factor.
Factors of 60 = 2 × 2 × 3 × 5 Factors of 100 = 2 × 2 × 5 × 5 Dividing the fraction by the common factors = 2 × 2 × 5 = 20 = 3/5
0.05 = 5/100 Dividing the fraction by 5, we get: 1/20
Dividing the fraction by 25, we get: (25 × 3)/ (25 × 4) = 3/4
Dividing the fraction by 2, we get: (2 × 9)/ (2 × 50) = 9/50
Dividing the fraction by 25, we get: (25 × 1)/ (25 × 4) = 1/4
Dividing the fraction by 125, we get: (125 × 1)/ (125 × 8) = 1/8
Dividing the fraction by 2, we get: (2 × 33)/ (2 × 500) = 33/500 ## Exercise 8.3
4/10 > 3/10
0.07 > 0.02 7/100 > 2/100
3 > 0.8 The decimal value (0.8) is less than the whole number 3.
5/10 > 5/100 1/10 is greater than 1/100.
Multiply both numbers by 100. 2.23 × 100 > 1.2 × 100 123 > 120 Hence, 1.23 is greater than 1.2.
Multiply both the numbers by 1000. 0.099 × 1000 = 99 0.19 × 1000 = 190 Thus, 190 > 99 0.19 > 0.099 Or 0.099 < 0.19
Let's multiply both the numbers by 100. 1.5 × 100 = 150 1.50 × 100 = 150 Thus, 1.5 = 1.50 The zero after the decimal value does not change the value of the number. For example, 2.0 = 2 2.22 = 2.2200
1.431 × 1000 = 1431 1.490 × 1000 = 1490 Thus, 1431 < 1490 Or 1.431 < 1.490
The zero after the decimal value does not change the value of the number. For example, 4.55 = 4.5500 2.0 = 2.000
5.64 × 1000 = 5640 5.603 × 1000 = 5603 Thus, 5640 > 5603 5.64 > 5.603
The five examples are given below: - 0.2 < 0.6
- 0.20 > 0.020
- 0.5 < 0.9
- 4.4 < 6.4
- 2.00 > 0.20
## Exercise 8.4
1 rupee = 100 paisa 1 paisa = 1/100 rupee 1 paisa = 0.01 rupee
5 paisa = 5 × 0.01 = 0.05 rupee
75 paisa = 75 × 0.01 = 0.75 rupee
20 paisa = 20 × 0.01 = 0.20 rupee
90 piasa = 90 × 0.01 = 0.90 rupee 50 rupee + 0.90 rupee = 50.90 rupee
725 paisa = 725 × 0.01 = 7.25 rupee = 7 rupee and 0.25 paisa
1m = 100 cm 1 cm = 1/100 m 1 cm = 0.01 m
1 cm = 0.01 m 15 cm = 15 × 0.01 m = 0.15 m
1 cm = 0.01 m 6 cm = 6 × 0.01 m = 0.06 m
1 cm = 0.01 m 45 cm = 45 × 0.01 m = 0.45 m 2 m + 45 cm = 2 m + 0.45 m = 2.45 m
1 cm = 0.01 m 7 cm = 7 × 0.01 m = 0.07 m 9m 7 cm = 9 m + 0.07 m = 9.07 m
1 cm = 0.01 m 419 cm = 419 × 0.01 m = 4.19 m = 4 m and 19 cm
1 cm = 10 mm 1 mm = 1/10 cm 1 mm = 0.1 cm
1 mm = 0.1 cm 5 mm = 0.1 × 5 = 0.5 cm
1 mm = 0.1 cm 60 mm = 0.1 × 60 = 6.0 cm
1 mm = 0.1 cm 164 mm = 0.1 × 164 = 16.4 cm
1 mm = 0.1 cm 8 mm = 0.1 × 8 = 0.8 cm 9 cm + 0.8 cm = 9.8 cm
1 mm = 0.1 cm 93 mm = 0.1 × 93 = 9.3 cm
1 km = 1000m 1 m = 1/1000 km 1m = 0.001 km
1m = 0.001 km 8 m = 0.001 × 8 = 0.008 km
1m = 0.001 km 88 m = 0.001 × 88 = 0.088 km
1m = 0.001 km 8888 m = 0.001 × 8888 = 8.888 km
1m = 0.001 km 5 m = 0.001 × 5 = 0.005 km 70 km 5 m = 70 km + 0.005 km = 70.005 km
1 kg = 1000 g 1 g = 1/1000 kg 1g = 0.0001 kg
1g = 0.0001 kg 2 g = 0.001 × 2 = 0.002 kg
1g = 0.0001 kg 100 g = 0.001 × 100 = 0.1 kg
1g = 0.0001 kg 3750 g = 0.001 × 3750 = 3.750 kg = 3.75 kg
1g = 0.0001 kg 8 g = 0.001 × 8 = 0.008 kg 5 kg 8 g = 5 kg + 0.008 kg = 5.008 kg
1g = 0.0001 kg 50 g = 0.001 × 50 = 0.05 kg 26 kg 50 g = 26 kg + 0.05 kg = 26.05 kg ## Exercise 8.5
(a) 0.007 + 8.5 + 30.08
(b) 15 + 0.632 + 13.8
(c) 27.076 + 0.55 + 0.004
(d) 25.65 + 9.005 + 3.7
(e) 0.75 + 10.425 + 2
(f) 280.69 + 25.2 + 38
Total rupees spent by Rashid for Maths book = 35.75 Total rupees spent by Rashid for Science book = 32.60 Total amount spent by Rashid = Rupees spent for Maths book + Rupees spent for Science book Total amount spent by Rashid = 35.75 + 32.60 = 68.35 Thus, the total amount spent by Rashid is rupees 68.35.
Rupees given to Radhika by her mother = 10.50 Rupees given to Radhika by her father = 15.80 Total amount = 10.50 + 15.80 = 26.30 Thus, the total amount given to Radhika by her parents is 26.30 rupees.
Cloth bought by Nasreen for her skirt = 3 m 20 cm Cloth bought by Nasreen for her trouser = 2 m 5 cm Total length of cloth = 3 m 20 cm + 2 m 5 cm = 5m 25 cm Thus, the total length of cloth bought by Nasreen is equal to 5.25 m.
Distance walked by Naresh in the morning = 2 km 35 m Distance walked by Naresh in the evening = 1 km 7 m Total distance = 2 km 35 m + 1 km 7 m = 3 km 42 m 1 km = 1000 m 1m = 1/1000 km 42 m = 42/1000 = 0.042 km 3 km + 0.042 km = 3.042 km Thus, the total distance walked by Naresh is 3.042 km.
Distance travelled by Sunita by bus = 15 km 268 m Distance travelled by Sunita by car = 7 km 7 m Distance travelled by Sunita on foot = 500 m Total distance = 15 km 268 m + 7 km 7 m + 500 m = (15 + 7) km (268 + 7 + 500) m = 22 km 775m 575 m = 0.775 km Total distance = 22 km + 0.775 km = 22.775 km Thus, Sunita's school is 22.775 km far from her residence.
Weight of rice purchased by Ravi = 5 kg 400 g Weight of sugar purchased by Ravi = 2 kg 20 g Weight of flour purchased by Ravi = 10 kg 850g Total weight = 5 kg 400 g + 2 kg 20 g + 10 kg 850g = (5 + 2 + 10) kg (400 + 20 + 850)g = 17 kg 1270 g 1 kg = 1000 g 1270 g = 1.270 kg Total weight = 17 kg + 1.270 kg = 18.270 kg Thus, the total weight of his purchases is 18.270 kg. ## Exercise 8.6
(a) 18.25 from 20.75
20.75 - 18.25 = (b) 202.54 m from 250 m
250 - 202.54 = 250.00 m - 202.54 m = (c) 5.36 from 8.40
8.40 - 5.36 = (d) 2.051 km from 5.206 km
5.206 km - 2.051 km = (e) 0.314 kg from 2.107 kg
2.107 kg - 0.314 kg =
(a) 9.756 - 6.28
(b) 21.05 - 15.27
(c) 18.5 - 6.79
(d) 11.6 - 9.847
Price of a book bought by Raju = 35.65 Amount given to the shopkeeper = 50 Money left = 50 - 35.65 = 14.35 Thus, Raju got rupees 14.35 back from the shopkeeper.
Price of ice-cream bought by Rani = 11.75 Total amount with Rani = 18.50 Amount left = 18.50 - 11.75 = 6.75 Thus, Rani have rupees 6.27 left with her.
Total length of the cloth = 20 m 5 cm = 20.05 m (1 m = 100 cm) Length of the cut out cloth to make a curtain = 4 m 50 cm = 4.50 m Cloth left = 20.05 m - 4.50 m = 15.55 m Thus, 15.55 m of cloth was left with Tina.
Distance travelled by Namita everyday = 20 km 50 m Distance travelled by Namita by bus = 10 km 200 m Distance travelled by Namita by auto = Total distance - Distance by bus = 20 km 50 m - 10 km 200 m = 20.050 km - 10.200 km (1 km = 1000m) = 9.850 km
Weight of vegetables bought by Aakash = 10 kg Weight of onions = 3 kg 500 g = 3.5 kg or 3.500 kg Weight of tomatoes = 2 kg 75 g = 2.075 kg Weight of potatoes = Total weight - (Weight of onions + weight of tomatoes) = 10 kg - (3.500 kg + 2.075 kg) = 10 kg - 5.575 kg = 4.425 kg Thus, the total weight of the potatoes is 4.425 kg. Next TopicClass 6 Maths Chapter 9 |