NCERT Solutions for Class 6 Maths - Decimals

Exercise 8.1 

Q1. Which is greater: 
(a) 0.3 or 0.4 
(b) 0.07 or 0.02 
(c) 3 or 0.8 
(d) 0.5 or 0.05 
(e) 1.23 or 1.2 
(f) 0.099 or 0.19 
(g) 1.5 or 1.50 
(h) 1.431 or 1.490 
(i) 3.3 or 3.300 
(j) 5.64 or 5.603 
Ans: 

(a) 0.3 or 0.4
Compare digits from the leftmost place value.
Whole parts (units) are equal (0 and 0). Compare tenths: 0.3 has 3 tenths, 0.4 has 4 tenths.
∴ 0.4 > 0.3

(b) 0.07 or 0.02
Whole parts and tenths are equal (0 and 0). Compare hundredths: 0.07 has 7 hundredths, 0.02 has 2 hundredths.
∴ 0.07 > 0.02

(c) 3 or 0.8
Compare whole parts: 3 (units) is greater than 0 (in 0.8).
∴ 3 > 0.8

(d) 0.5 or 0.05
Whole parts are equal (0). Compare tenths: 0.5 has 5 tenths, 0.05 has 0 tenths and 5 hundredths.
∴ 0.5 > 0.05

(e) 1.23 or 1.20
Whole parts and tenths are equal (1 and 2 tenths). Compare hundredths: 1.23 has 3 hundredths, 1.20 has 0 hundredths.
∴ 1.23 > 1.20

(f) 0.099 or 0.19
Whole parts and tenths: 0.099 has 0 tenths, 0.19 has 1 tenth. Since 1 tenth > 0 tenths, 0.19 is larger.
∴ 0.099 < 0.19

(g) 1.5 or 1.50
Write missing places as zeros: 1.5 = 1.50. All corresponding place values are equal.
∴ 1.5 = 1.50

(h) 1.431 or 1.490
Whole parts and tenths are equal (1 and 4 tenths). Compare hundredths: 1.431 has 3 hundredths, 1.490 has 9 hundredths. Since 9 > 3,
∴ 1.431 < 1.490

(i) 3.3 or 3.300
Write missing places as zeros: 3.3 = 3.300. All corresponding place values are equal.
∴ 3.3 = 3.300

(j) 5.64 or 5.603
Whole parts and tenths are equal (5 and 6 tenths). Compare hundredths: 5.64 has 4 hundredths, 5.603 has 0 hundredths (and 3 thousandths). Since 4 hundredths > 0 hundredths,
∴ 5.64 > 5.603

Q2. Make five more examples and find the greater: 
(a) 1.8 or 1.82 
(b) 1 or 0.99
(c) 1.09 or 1.093 
(d) 2 or 1.99
(e) 2.08 or 2.085
Ans:

(a) 1.82 or 1.8
Whole parts equal (1). Tenths equal (8). Compare hundredths: 1.82 has 2 hundredths while 1.8 has 0 hundredths (1.80).
Hence, 1.82 > 1.8

(b) 1 or 0.99
Compare whole parts: 1 has unit 1, while 0.99 has unit 0.
∴ 1 > 0.99

(c) 1.09 or 1.093
Whole, tenths and hundredths are equal (1, 0 and 9 hundredths). Compare thousandths: 1.093 has 3 thousandths while 1.09 has 0 thousandths (1.090).
∴ 1.093 > 1.09

(d) 2 or 1.99
Compare whole parts: 2 (unit 2) > 1 (in 1.99).
∴ 2 > 1.99

(e) 2.08 or 2.085
Whole, tenths and hundredths: 2.08 has 0 hundredths = 8 hundredths, 2.085 has an extra 5 thousandths (2.085 = 2.085). Compare thousandths: 2.085 has 5 thousandths, 2.080 has 0 thousandths.
∴ 2.085 > 2.08

Exercise 8.2

Q1. Express as rupees using decimals: 
(a) 5 paise 
(b) 75 paise 
(c) 20 paise 
(d) 50 rupees 90 paise 
(e) 725 paise 
Ans: We know that there are 100 paise in 1 rupee.
(a) 5 paise = 5 / 100 rupees = Rupees 0.05
(b) 75 paise = 75 / 100 rupees = Rupees 0.75
(c) 20 paise = 20 / 100 rupees = Rupees 0.20
(d) 50 rupees 90 paise = 50 + 90/100 rupees = Rupees 50.90
(e) 725 paise = 725 / 100 rupees = Rupees 7.25

Q2. Express as meters using decimals: 
(a) 15 cm 
(b) 6 cm 
(c) 2 m 45 cm 
(d) 9 m 7 cm 
(e) 419 cm 
Ans: We know that there are 100 cm in 1 metre.
(a) 15 cm = 15 / 100 m = 0.15 m
(b) 6 cm = 6 / 100 m = 0.06 m
(c) 2 m 45 cm = 2 + 45/100 m = 2.45 m
(d) 9 m 7 cm = 9 + 7/100 m = 9.07 m
(e) 419 cm = 419 / 100 m = 4.19 m

Q3. Express as cm using decimals: 
(a) 5 mm 
(b) 60 mm 
(c) 164 mm 
(d) 9 cm 8 mm 
(e) 93 mm 
Ans: We know that there are 10 mm in 1 cm.
(a) 5 mm = 5 / 10 cm = 0.5 cm
(b) 60 mm = 60 / 10 cm = 6.0 cm
(c) 164 mm = 164 / 10 cm = 16.4 cm
(d) 9 cm 8 mm = 9 + 8/10 cm = 9.8 cm
(e) 93 mm = 93 / 10 cm = 9.3 cm

Q4. Express as km using decimals: 
(a) 8 m 
(b) 88 m 
(c) 8888 m 
(d) 70 km 5 m 
Ans: We know that there are 1000 metres in 1 km.
(a) 8 m = 8 / 1000 km = 0.008 km
(b) 88 m = 88 / 1000 km = 0.088 km
(c) 8888 m = 8888 / 1000 km = 8.888 km
(d) 70 km 5 m = 70 + 5/1000 km = 70.005 km

Q5. Express as kg using decimals: 
(a) 2 g 
(b) 100 g 
(c) 3750 g 
(d) 5 kg 8 g 
(e) 26 kg 50 g 
Ans: We know that there are 1000 grams in 1 kg.
(a) 2 g = 2 / 1000 kg = 0.002 kg
(b) 100 g = 100 / 1000 kg = 0.100 kg (often written as 0.1 kg)
(c) 3750 g = 3750 / 1000 kg = 3.750 kg
(d) 5 kg 8 g = 5 + 8/1000 kg = 5.008 kg
(e) 26 kg 50 g = 26 + 50/1000 kg = 26.050 kg

Exercise 8.3

Q1. Find the sum in each of the following:
(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
Ans:

Q2. Rashid spent Rs 35.75 for Maths book and Rs 32.60 for Science book. Find the total amount spent by Rashid.
Ans: Money spent for Maths book = Rs 35.75
Money spent for Science book = Rs 32.60
Total money spent = Rs 35.75 + Rs 32.60
= Rs 68.35
Therefore, total money spent by Rashid is Rs 68.35.

Q3. Radhika's mother gave her Rs10.50 and her father gave her Rs15.80. Find the total amount given to Radhika by the parents.
Ans: Money given by mother = Rs 10.50
Money given by father = Rs 15.80
Total money received = Rs 10.50 + Rs 15.80
= Rs 26.30
Therefore, the total money received by Radhika is Rs 26.30.

Q4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of cloth bought by her.
Ans: Cloth bought for shirt = 3 m 20 cm = 3.20 m
Cloth bought for trouser = 2 m 5 cm = 2.05 m
Total length of cloth = 3.20 + 2.05
= 5.25 m
Therefore, the total length of cloth bought by Nasreen is 5.25 m.

Q5. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he walk in all?
Ans: Distance in morning = 2 km 35 m = 2.035 km
Distance in evening = 1 km 7 m = 1.007 km
Total distance = 2.035 + 1.007
= 3.042 km
Therefore, the total distance travelled by Naresh is 3.042 km.

Q6. Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m by foot in order to reach her school. How far is her school from her residence?
Ans: Distance by bus = 15 km 268 m = 15.268 km
Distance by car = 7 km 7 m = 7.007 km
Distance on foot = 500 m = 0.500 km
Total distance = 15.268 + 7.007 + 0.500
= 22.775 km
Therefore, total distance travelled by Sunita is 22.775 km.

Q7. Ravi purchases 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour. Find the total weight of his purchases.
Ans: Weight of rice = 5 kg 400 g = 5.400 kg
Weight of sugar = 2 kg 20 g = 2.020 kg
Weight of flour = 10 kg 850 g = 10.850 kg
Total weight = 5.400 + 2.020 + 10.850
= 18.270 kg
Therefore, the total weight of Ravi's purchase = 18.270 kg.

Exercise 8.4

Q1. Subtract:

(a) Rs. 18.25 from Rs. 20.75

(b) 202.54 m from 250

(c) Rs. 5.36 from Rs. 8.40

(d) 2.051 km from 5.206 km

(e) 0.314 kg from 2.107 kg

Ans:

Q2. Find the value of:
(a) 9.756 - 6.28
(b) 21.05 - 15.27
(c) 18.5 - 6.79
(d) 11.6 - 9.847
Ans:

Q3. Raju bought a book of Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?
Ans: Total amount given = Rs 50.00
Cost of book = Rs 35.65
Change = Rs 50.00 - Rs 35.65
= Rs 14.35
Therefore, Raju got back Rs 14.35 from the shopkeeper.

Q4. Rani had Rs18.50. She bought one ice-cream for Rs11.75. How much money does she have now
Ans: Total money = Rs 18.50
Cost of ice-cream = Rs 11.75
Remaining money = Rs 18.50 - Rs 11.75
= Rs 6.75
Therefore, Rani has Rs 6.75 now.

Q5. Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?
Ans: Total cloth = 20 m 5 cm = 20.05 m
Cloth used = 4 m 50 cm = 4.50 m
Remaining cloth = 20.05 - 4.50
= 15.55 m
Therefore, 15.55 m of cloth is left with Tina.

Q6. Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?
Ans: Total distance = 20 km 50 m = 20.050 km
Distance by bus = 10 km 200 m = 10.200 km
Distance by auto = 20.050 - 10.200
= 9.850 km
Therefore, 9.850 km is travelled by auto.

Q7. Aakash bought vegetables weighing 10 kg. Out of this 3 kg 500 g in onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
Ans: Weight of onions = 3 kg 500 g = 3.500 kg
Weight of tomatoes = 2 kg 75 g = 2.075 kg
Total of onions and tomatoes = 3.500 + 2.075
= 5.575 kg
Total vegetables = 10.000 kg
Weight of potatoes = 10.000 - 5.575
= 4.425 kg
Thus, the weight of potatoes is 4.425 kg.