NCERT Solutions for Chapter 8 Decimals Class 6 Maths
Decimals Questions and Answers
Chapter Name | Decimals NCERT Solutions |
Class | CBSE Class 6 |
Textbook Name | Maths |
Related Readings |
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Exercise 8.1
Question 1: Write the following as numbers in the given table:
Hundreds (100) | Tens (10) | Ones (1) | Tenths (1/10) |
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hundreds (100) |
Tens (10) |
Ones (1) |
Tenths (1/10) |
|
0 |
3 |
2 |
31.2 |
|
1 |
1 |
4 |
110.4 |
Question 2: Write the following decimals in the place value table:
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9
Solution
(a)|
hundreds
|
Tens
|
Ones
|
Tenths
|
|
0 |
1 |
9 |
4 |
(b)
|
hundreds
|
Tens
|
Ones
|
Tenths
|
|
0 |
0 |
0 |
3 |
|
hundreds
|
Tens
|
Ones
|
Tenths
|
|
0 |
1 |
0 |
6 |
(d)
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hundreds
|
Tens
|
Ones
|
Tenths
|
|
2 |
0 |
5 |
9 |
Question 3: Write each of the following as decimals:
(a) seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two-ones
(e) Six hundred point eight
Solution
(a) seven-tenths = 7 tenths = 7/10 = 0.7
(b) 2 tens and 9-tenths = 2×10 +9/10 = 20 + 0.9 =20.9
(c) Fourteen point six = 14.6
(d) One hundred and 2-ones = 100 + 2×1 = 100 + 2 = 102
(e) Six hundred point eight = 600.8
Question 4: Write each of the following as decimals:
Solution
(a) 5/10
(b) 3+7/10
(c) 200+60++5+1/10
(d) 70+8/10
(e) 88/10
(g) 3/2
(h) 2/5
(i) 12/5
Solution
(a) 5/10 = 0.5
(b) 3+7/10 = 3 + 0.7 = 3.7
(c) 200+60+5+1/10 = 200 + 60 + 5 + 0.1 = 265.1
(d) 70+8/10 = 70 + 0.8 = 70.8
(h) 2/5 = 2×2/5×2 = 4/10 = 0.4
(a) 0.6
(b) 2.5
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4
Solution
Question 6: Express the following as cm using decimals:
(a) 2 mm
(b) 30 mm
(c) 116 mm
(d) 4 cm 2 mm
(e) 162 mm
(f) 83 mm
Solution
(a) ∵ 10 mm = 1 cm
∴ 1 mm = 1/10 cm
∴ 2 mm = 1/10×2 = 0.2 cm
(b) ∵ 10 mm = 1 cm
∴ 1 mm = 1/10 cm
∴ 30 mm = 1/10×30 = 3.0 cm
(c) ∵ 10 mm = 1 cm
∴ 1 mm = 1/10 cm
∴ 116 mm = 1/10×116 = 11.6 cm
(d) 4 cm+2/10 cm [∵ 10 mm = 1cm]
4+0.2 = 4.2 cm
(e) ∵ 10 mm = 1 cm
∴ 1 mm = 1/10 cm
∴ 162 mm = 1/10×162 = 16.2 cm
(f) ∵ 10 mm = 1 cm
∴ 1 mm = 1/10 cm
∴ 83 mm = 1/10×83 = 8.3 cm
Question 7: Between which two whole numbers on the number line are the given lie? Which of these whole numbers is nearer the number?
(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9
Solution
(a) From 0 to 1, 0.8 is nearest to 1.
(b) From 5 to 6, 5.1 is nearest to 5.
(c) From 2 to 3, 2.6 is nearest to 3.
(d) From 6 to 7, 6.4 is nearest to 6.
(e) From 9 to 10, 9.1 is nearest to 9.
(f) From 4 to 5, 4.9 is nearest to 5.
Question 8: Show the following numbers on the number line:
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5
Solution
Question 9: Write the decimal number represented by the points A, B, C, D on the given number line.
Solution
A = 0 + 8/10 = 0.8
B = 1 + 3/10 = 1.3
C = 2 + 2/10 = 2.2
D = 2 + 9/10 = 2.9
Question 10: (a) The length of Ramesh’s notebook is 9 cm and 5 mm. What will be its length in cm?
(b) The length of a young gram plant is 65 mm. Express its length in cm.
Solution
(a) 9 cm 5 mm = 9 cm + 5 mm = 9 + 5/10 = 9.5 cm
(b) 65 mm = 65/10 cm = 6.5 cm
Exercise 8.2
Question 1: Complete the table with the help of these boxes and use decimals to write the number:
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Ones |
Tenths |
Hundredths |
Number |
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(a) |
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(b) |
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(c) |
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Solution
|
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Ones |
Tenths |
Hundredths |
Number |
|
(a) |
0 |
2 |
6 |
0.26 |
|
(b) |
1 |
3 |
8 |
1.38 |
|
(c) |
1 |
2 |
9 |
1.29 |
Question 2: Write the numbers given in the following place value table in decimal form:
|
|
Hundreds (100) |
Tens (10) |
Ones (1) |
Tenths (1/10) |
Hundredths (1/100) |
Thousandths (1/1000) |
|
(a) |
0 |
0 |
3 |
2 |
5 |
0 |
|
(b) |
1 |
0 |
2 |
6 |
3 |
0 |
|
(c) |
0 |
3 |
0 |
0 |
2 |
5 |
|
(d) |
2 |
1 |
1 |
9 |
0 |
2 |
|
(e) |
0 |
1 |
2 |
2 |
4 |
1 |
Solution
(a) 0 × 100 + 0 × 10 + 3 × 1 + 2 × 1/10 + 5 × 1/100 + 0 × 1/1000
= 0 + 0 + 3 + 0.2 + 0.05 + 0 = 3.25
(b) 1 × 100 + 0 × 10 + 2 × 1 + 6 × 1/10 + 3 × 1/100 + 0 × 1/1000
= 1 + 0 + 2 + 0.6 + 0.03 + 0 = 102.63
(c) 0 × 100 + 3 × 10 + 0 × 1 + 0 × 1/10 + 2 × 1/100 + 5 × 1/1000
= 0 + 30 + 0 + 0 + 0.02 + 0.005 = 30.025
(d) 2 × 100 + 1 × 10 + 1 × 1 + 9 × 1/10 + 0 × 1/100 + 2 × 1/1000
= 200 + 10 + 1 + 0.9 + 0 + 0.002 = 211.902
(e) 0 × 100 + 1 × 10 + 2 × 1 + 2 × 1/10 + 4 × 1/100 + 1 × 1/1000
=0 + 10 + 2 + 0.2 + 0.04 + 0.001 = 12.241
Question 3: Write the following decimals in the place value table:
(a) 0.29
(b) 2.08
(c) 19.60
(d) 148.32
(e) 200.812
Solution
|
|
Numbers |
Hundreds (100) |
Tens (10) |
Ones (1) |
Tenths (1/10) |
Hundredths (1/100) |
Thousandths (1/1000) |
|
(a) |
0.29 |
0 |
0 |
0 |
2 |
9 |
0 |
|
(b) |
2.08 |
1 |
0 |
2 |
0 |
8 |
0 |
|
(c) |
19.60 |
0 |
1 |
9 |
6 |
0 |
0 |
|
(d) |
148.32 |
1 |
4 |
8 |
3 |
2 |
0 |
|
(e) |
200.812 |
2 |
0 |
0 |
8 |
1 |
2 |
Question 4: Write each of the following as decimals:
(a) 20+9+4/10+1/100
(b) 137+5/100
(c) 7/10+6/100+4/1000
(d) 23+2/10+6/1000
(e) 700+20+5+9/100
Solution
(a) 20 + 9 + 0.4 + 0.01 = 29.41
(b) 137 + 0.05 = 137.05
(c) 0.7 + 0.06 + 0.004 = 0.764
(d) 23 + 0.2 + 0.006 = 23.206
(e) 700 + 20 + 5 + 0.09 = 725.09
Question 5: Write each of the following decimals in words:
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10.07
(e) 0.032
(f) 5.008
Solution
(a) Zero point zero three
(b) One point two zero
(c) One hundred and eight point five six
(d) Ten point zero seven
(e) Zero point zero three two
(f) Five point zero zero eight
Question 6: Between which two numbers in tenths place on the number line does each of the given number lie?
(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57
Solution
All the numbers lie between 0 and 1.
(a) 0.06 is nearer to 0.1.
(b) 0.45 is nearer to 0.5.
(c) 0.19 is nearer to 0.2.
(d) 0.66 is nearer to 0.7.
(e) 0.92 is nearer to 0.9.
(f) 0.57 is nearer to 0.6.
Question 7: Write as fractions in lowest terms:
(a) 0.60
(b) 0.05
(c) 0.75
(d) 0.18
(e) 0.25
(f) 0.125
(g) 0.066
Solution
Question 1: 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
Solution
Before comparing, we write both terms in like decimals:
(a) 0.3 < 0.4
(b) 0.07 > 0.02
(c) 3.0 or 0.8 = 3.0 > 0.8
(d) 0.50 or 0.05 = 0.50 > 0.05
(e) 1.23 or 1.20 = 1.23 > 1.20
(f) 0.099 or 0.190 = 0.099 < 0.190
(g) 1.50 or 1.50 = 1.50 = 1.50
(h) 1.431 < 1.490
(i) 3.300 or 3.300 = 3.300 = 3.300
(j) 5.640 or 5.603 = 5.640 > 5.603
Question 2: Make five more examples and find the greater:
(a) 1.8 or 1.82
(b) 1.0009 or 1.09
(c) 10.01 or 100.1
(d) 5.100 or 5.0100
(e) 04.213 or 0421.3
Solution
Before comparing, we write both terms in like decimals
(a) 1.80 or 1.82 = 1.82 is greater than 1.8
(b) 1.0009 or 1.0900 = 1.09 is greater than 1.0009
(c) 10.01 or 100.10 = 100.1 is greater than 10.01
(d) 5.1000 or 5.0100 = 5.100 is greater than 5.0100
(e) 04.213 or 0421.300 = 0421.3 is greater than 04.213
Exercise 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) ∵ 1 paisa = ₹ 1/100
∴ 5 paise = 1/100 × 5 = ₹ 0.05
(b) ∵ 1 paisa = ₹ 1/100
∴ 75 paise = 1/100 × 5 = ₹ 0.75
(c) ∵ 1 paisa = ₹ 1/100
∴ 20 paise = 1/100 × 5 = ₹ 0.05
(d) ∵ 1 paisa = ₹ 1/100
∴ ₹ 50+90paise=50+ 1/100 × 90 =₹50.90
(e) ∵ 1 paisa = ₹ 1/100
∴ 725 paise = 1/100 × 725 = 725/100 = ₹ 7.25
Question 2: Express as meters using decimals:
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
(e) 419 cm
Solution
(a) ∵ 1 cm = 1/100 m
∴ 15 cm = 1/100 × 15 = 0.15 m
(b) ∵ 1 cm = 1/100 m
∴ 6 cm = 1/100 × 6 = 0.06 m
(c) ∵ 1 cm = 1/100 m
∴ 2 m 45 cm = 2 + 1/100 × 45 = 2.45 m
(d) ∵ 1 cm = 1/100 m
∴ 9 m 7 cm = 9 + 1/100 × 7 = 9.07 m
(e) ∵ 1 cm = 1/100 m
∴ 419 cm = 1/100 × 419 = 419/100 = 4.19 m
Question 3: Express as cm using decimals:
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm
Solution
(a) ∵ 1 mm = 1/10 cm
∴ 5 mm = 1/10 × 5 = 0.5 cm
(b) ∵ 1 mm = 1/10 cm
∴ 60 mm = 1/10 × 60 = 6 cm
(c) ∵ 1 mm = 1/10 cm
∴ 164 mm = 1/10 × 164 = 16.4 cm
(d) ∵ 1 mm = 1/10 cm
∴ 9cm 8mm = 9+ 1/10 × 8 =9+0.8=9.8 cm
(e) ∵ 1 mm = 1/10 cm
∴ 93 mm = 1/10 × 93 = 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) ∵ 1 m = 1/1000 km
∴ 8 m = 1/1000 × 8 = 0.008 km
(b) ∵ 1 m = 1/1000 km
∴ 88 m = 1/1000 × 88 = 0.088 km
(c) ∵ 1 m = 1/1000 km
∴ 8888 m = 1/1000 × 8888 = 8.888 km
(d) ∵ 1 m = 1/1000 km
∴ 70 km 5m =70+ 1/1000 × 5 =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) ∵ 1 g = 1/1000 kg
∴ 2 g = 1/1000 × 2 = 0.002 kg
(b) ∵ 1 g = 1/1000 kg
∴ 100 g = 1/1000 × 100 = 0.1 kg
(c) ∵ 1 g = 1/1000 kg
∴ 3750 g = 1/1000 × 3750 = 3.750 kg
(d) ∵ 1 g = 1/1000 kg
∴ 5 kg 8 g = 5 + 1/1000 × 8 = 5.008 kg
(e) ∵ 1 g = 1/1000 kg
∴ 26 kg 50 g = 26 + 1/1000 × 50 = 26.050 kg
Exercise 8.5
Question 1: 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
Solution
Solution
Money spent for Maths book = ₹35.75
Money spent for Science book = ₹32.60
Total money spent = ₹35.75 + ₹32.60 = ₹68.35
Therefore, total money spent by Rashid is ₹68.35.
Question 3: Radhika’s mother have her ₹10.50 and her father gave her ₹15.80. Find the total amount given to Radhika by the parents.
Solution
Money given by mother = ₹10.50
Money given by father = ₹15.80
Total money received by Radha = ₹10.50 + ₹15.80 = ₹26.30
Therefore, the total money received by Radha is ₹26.30.
Question 4: 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.
Solution
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 bought by Nasreen = 3.20 + 2.05 = 5.25 m
Therefore, the total length of cloth bought by Nasreen is 5.25 m
Question 5: 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?
Solution
Distance travelled in morning = 2 km 35 m = 2.035 km
Distance travelled in evening = 1 km 7 m = 1.007 km
Total distance travelled = 2.035 + 1.007 = 3.042 km
Therefore, the total distance travelled by Naresh is 3.042 km.
Question 6: 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?
Solution
Distance travelled by bus = 15 km 268 m = 15.268 km
Distance travelled by car = 7 km 7 m = 7.007 km
Distance travelled on foot = 500 m = 0.500 km
Total distance travelled = 15.268 + 7.007 + 0.500 = 22.775 km
Therefore, total distance travelled by Sunita is 22.775 km.
Question 7: 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.
Solution
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 8.6
Question 1: Subtract:
(a) ₹18.25 from ₹20.75
(b) 202.54 m from 250
(c) ₹5.36 from ₹8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg
Solution
(a) 9.756 – 6.28
(b) 21.05 – 15.27
(c) 18.5 – 6.79
(d) 11.6 – 9.847
Solution
Question 3: Raju bought a book of ₹35.65. He gave ₹50 to the shopkeeper. How much money did he get back from the shopkeeper?
Solution
Total amount given to shopkeeper = ₹50
Cost of book = ₹35.65
Amount left = ₹50.00 – ₹35.65
= ₹14.35
Therefore, Raju got back ₹14.35 from the shopkeeper.
Question 4: Rani had ₹18.50. She bought one ice-cream for ₹11.75. How much money does she have now?
Solution
Total money = ₹18.50
Cost of Ice-cream = ₹11.75
Amount left = ₹18.50 – ₹11.75
= ₹6.75
Therefore, Rani has ₹6.75 now.
Question 5: 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?
Solution
Total length of cloth = 20 m 5 cm = 20.05 m
Length of cloth used = 4 m 50 cm = 4.50 m
Remaining cloth = 20.05 m – 4.50 m = 15.55 m
Therefore, 15.55 m of cloth is left with Tina.
Question 6: 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?
Solution
Total distance travel = 20 km 50 m = 20.050 km
Distance travelled by bus = 10 km 200 m = 10.200 km
Distance travelled by auto = 20.050 – 10.200 = 9.850 km
Therefore, 9.850 km distance travels by auto.
Question 7: 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?
Solution
Weight of onions = 3 kg 500 g = 3.500 kg
Weight of tomatoes = 2 kg 75 g = 2.075 kg
Total weight of onions and tomatoes = 3.500 + 2.075 = 5.575 kg
Therefore, weight of potatoes = 10.000 – 5.575 = 4.425 kg
Thus, the weight of potatoes is 4.425 kg.