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NCERT Solutions for class 6 Maths chapter 8 – Decimals


Back Exercise

Exercise 8.1

Question 1.
Write the following as numbers in the given table:
(a)
NCERT Solutions for Class 6 Maths Chapter 8 Decimals
(b)
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 1

Hundreds
(100)
Tens
(10)
Ones
(1)

Tenths
(Undefined control sequence \cfrac)

Solution.

Hundreds
(100)
Tens
(10)
Ones
(1)
Tenths
(Undefined control sequence \cfrac)
(a) 0 3 1 2
(b)  1 1 0 4

Question 2.
Write the following decimals in the place value table :
(a)
19.4
(b)
0.3
(c)
10.6
(d)
05.9
Solution.

Hundreds Tens
Ones Tenths
(a) 0 1 9 4
(b)  0 0 0 3
(c)  0 1 0 6
(d)  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) 7 tenths : Undefined control sequence \cfrac =0.7.
(b) Two tens and nine-tenths = 20 + Undefined control sequence \cfrac  =20.9
(c) Fourteen point six = 14.6
(d) One hundred and two-ones =100 + 2=102
(e) Six hundred point eight = 600.8

Question 4.
Write each of the following as decimals:
(a) 
510
(b) 3 +710
(c) 200+60+5+110
(d) 70+810
(e) 210
(g) 32
(h) 25
(i) 125
(j) 35
(k) 412
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 2
tiwari academy class 6 maths Chapter 8 Decimals 3

Question 5.
Write the following decimals as fractions. Reduce the fractions to lowest form :
(a) 0.6
(b) 205
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4
Solution.
(a)
 Undefined control sequence \cfrac
∵  H.C.F.(6,10) = 2
= Undefined control sequence \cfrac

(b)
Undefined control sequence \cfrac
∵  H.C.F.(25,10) = 5
= Undefined control sequence \cfrac

(c)
Undefined control sequence \cfrac
∵  H.C.F.(10,10) = 10
= Undefined control sequence \cfrac =1

(d)
Undefined control sequence \cfrac
∵  H.C.F.(38,10) = 2
= Undefined control sequence \cfrac

(e)
Undefined control sequence \cfrac

(f)
Undefined control sequence \cfrac
∵  H.C.F.(212,10) = 5
= Undefined control sequence \cfrac

(g)
Undefined control sequence \cfrac
∵  H.C.F.(64,10) = 2
= Undefined control sequence \cfrac

Question 6.
Express the following as cm using decimals:
(a)
2mm
(b)
30mm
(c)
116mm
(d)
4cm2mm
(e)
11cm 52cm
(f)
83 mm
Solution.
(a)
Undefined control sequence \cfrac
∵  Undefined control sequence \cfrac
= 0.2cm

(b)
Undefined control sequence \cfrac
∵  Undefined control sequence \cfrac
= 3cm = 3.0cm
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 4
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 5
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 6

Question 7.
Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number?
(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.0
(f) 4.9
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 7
Solution.
(a) 0.8. The number 0.8 is between the two whole numbers 0 and 1. The whole number 1 is nearer the number 0.8.

(b) 5.1. The number 5.1 is between the two whole numbers 5 and 6. The whole number 5 is nearer the number 5.1.

(c) 2.6. The number 2,6 is between the two whole numbers 2 and 3. The whole number 3 is nearer the number 2.6.

(d) 6.4 The number 6.4 is between the two whole numbers 6 and 7. The whole number 6 is nearer the number 6.4.

(e) 0. 9.0 itself is a whole number.

(f) 4.9. The number 4.9 is between the two whole numbers 4 and 5. The whole number 5 is nearer the number 4.9.

Question 8.
Show the following numbers on the number line:
(a)
2
(b) 1.9
(c) 1
(d) 2.5.
Solution.
(a) 0.2. We know that 0.2 is more than zero but less than one. There are 2-tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 2 parts as shown below:
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 8

(b) 1.9. We know that 1.9 is more than one but less than two. There are 9-tenths in’it. Divide the unit length between 1 and 2 into 10 equal parts and take 9 parts as shown below:
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 9

(c) 1.1. We know that 1.1 is more than one but less than two. There is one-tenth in it. Divide the unit length between 1 and 2 into 10 equal parts and take 1 part as shown below:
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 10

(d) 2.5. We know that 2.5 is more than two but less than three. There are 5-tenths in it. Divide the unit length between 2 and 3 into 10 equal parts and take 5 parts as shown below :
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 11

Question 9.
Write the decimal number represented by the points A, B, C, D on the given number line :
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 12
Solution.
(i) A. The decimal number represented by the point A is 0.8 as the unit length between 0 and 1 has been divided into 10 equal parts and 8 parts have been taken.

(ii) B. The decimal number represented by the point B is 1.3 as the unit length between 1 and 2 has been divided into 10 equal parts and 3 parts have been taken.

(iii) C. The decimal number represented by the point C is 2.2 as the unit length between 2 and 3 has been divided into 10 equal parts and 2 parts have been taken.

(iv) D. The decimal number represented by the point D is 2.9 as the unit length between 2 and 3 has been divided into 10 equal parts and 9 parts have been taken.

Question 10.
(a) The length of Ramesh’s notebook is 9 cm 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) Length of Ramesh’s notebook = 9 cm 5mm
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 57

NCERT Solutions for Class 6 Maths Chapter 8 Decimals 13
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 14

Exercise 8.2

Question 1.
Complete the table with the help of these boxes and use decimals to write the number.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 15

Ones Tenths Hundredths Number
(a)
(b)
(c)

Solution.

Ones Tenths Hundredths Number
(a) 0 2 6 0.26
(b) 1 3 8 1.38
(c) 1 2 8 1.28

Question 2.
Write the numbers in the following place value table in decimal form:

Hundreds
(100)
Tens
(10)
ones
(1)
Tenths
(Tenths
Undefined control sequence \cfrac)

Hundredths
(Tenths
Undefined control sequence \cfrac)
Thousandths
(Tenths
Undefined control sequence \cfrac)
(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.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 16
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 17
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 18

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.

DecimalNumber Hundreds Tens Ones Tenths Hundredths Thousandths
(a) 0.29 0 0 0 2 9 0
(b) 2.08 0 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+410+1100
(b)
30+4108100
(c)
137+ 5100
(d) 
710610041000
(e) 23+21061000
(f)
700+20+5+9100
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 19
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 20

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 eight point five six
(d) Ten point zero seven
(e) Zero point zero three two
(f) Five point zero eight.

Question 6.
Between which two numbers in tenths place on the number line does each of the given number lie?
(a) 06
(b) 0.45
(c) 19
(d) 0.66
(e) 92
(f) 0.57.
Solution.
Each of the given numbers lies between the two whole numbers 0 and 1 on the number line.
(a) 0 and 0.1
(b) 4 and 0.5
(c) 1 and 0.2
(d)  0.6 and 0.7
(e) 9 and 1.0
(f)  0.5 and 0.6.

Question 7.
Write as fractions in lowest terms:
(a) 0.60
(b) 0.05
(c) 75
(d) 0.18
(e) 25
(f) 0.125.
Solution.
(a) 0.60
Undefined control sequence \cfrac
∵  H.C.F.(60,100) = 20
= Undefined control sequence \cfrac

(b) 0.05

Undefined control sequence \cfrac
∵  H.C.F.(5,100) = 5
= Undefined control sequence \cfrac

(c) 0.75
Undefined control sequence \cfrac
∵  H.C.F.(75,100) = 25
= Undefined control sequence \cfrac

(d) 0.18
Undefined control sequence \cfrac
∵  H.C.F.(18,100) = 2
= Undefined control sequence \cfrac

(e) 0.25
Undefined control sequence \cfrac
∵  H.C.F.(25,100) = 25
= Undefined control sequence \cfrac

(f) 0.125
Undefined control sequence \cfrac
∵  H.C.F.(125,1000) =125
= Undefined control sequence \cfrac

Exercise 8.3

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.
(a) 0.3 or 0.4
Whole part for both is 0.
Tenth part for 0.3 is 3 and for 0.4 is 4
∵ 4>3
∴ 0.4 > 0.3

(b) 07 or 0.02
Whole part for both is 0.
Tenth part for both is 0.
Hundredth part for 0.07 is 7 and for 0.02 is 2.
∵7>2
∴  0.07 > 0.02

(c) 3 or 0.8
Whole part for 3 is 3 and for 0.8 is 0.
∵ 3 >0
∴3 >0.8

(d) 5 or 0.05
Whole part for both is 0.
Tenth part for 0.5 is 5 and for 0.05 is 0.
∵ 5 >0
∴ 0.5 > 0.05

(e) 23 or 1.2
Whole part for both is 1.
Tenth part for both is 2.
Hundredth part for 1.23 is 3 and for 1.2 is 0 (as 1.2= 1.20)

(f) 0.099 or 0.19
Whole part for both is 0.
Tenth part for 0.099 is 0 and for 0.19 is 1.
∵ 1>0
∴ 0.19 >0.099

(g)1.5 or 1.50
Whole part for both is 1.
Tenth part for both is 5.
Hundredth part for both is 0 (as 1.5 = 1.50).
∴ 1.5=1.50

(h) 1431 or 490
Whole part for both is 1.
Tenth part for both is 4.
Hundredth part for 1.431 is 3 and for 1.490 is 9
∵ 9>3
∴ 1.490 >1.431

(i) 3 or 3.300
Whole part for both is 3.
Tenth part for both is 3.
Hundredth part for both is 0 (as 3.3 = 3.30).
Thousandth part for both is 0 (as 3.3 = 3.300).
∴ 3.3 = 3.300

(J) 5.64 or 5.603 
Whole part for both is 5.
Tenth part for both is 6.
Hundredth part for 5.64 is 4 and for 5.603 is 0.
∵ 4>0
∴ 5.64 > 5.603

Question 2.
Make five more examples and find the greater number from them.
Solution.
Five more examples are as follows:
Which is greater?
Ex. 1. 0.4 or 0.5
Ex. 2. 0.06 or 0.04
Ex. 3. 4 ox 0.9
Ex. 4. 0.6 or 0.06
Ex. 5. 0.063 or 0.22
Solution.
1.
0.4 or 0.5

Whole part for both = 0
Tenth part for 0.4 = 4
Tenth part for 0.5 = 5
∵ 5 >4
∴ 0.5 > 0.4

2.
0.06 or 0.04

Whole part for both = 0
Tenth part for both = 0
Hundredth part for 0.06 = 6
Hundredth part for 0.04 = 4
∵ 6 >4
∴ 0.06 > 0.04

3.
4 or 0.9
Whole part for 4 = 4
Whole part for 0.9 = 0
∵ 4 > 0
∴ 4 > 0.9

4.
0.6 or 0.06
Whole part for both = 0
Tenth part for 0.6 = 6
Tenth part for 0.06 = 0
∵  6 > 0
∴ 0.6 > 0.06

5.
0.063 or 0.22
Whole part for both = 0
Tenth part for 0.063 = 0
Tenth part for 0.22 = 2
∵  2 > 0
∴ 0.22 > 0.063.

Exercise 8.4

Question 1.
Express as rupees using decimals.
(a) 5 paise
(b) 75 paise
(c) 20 paise
(d) 50 rupees 90paise
(e) 725 paise.
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 21
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 22
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 24

Question 2.
Express as meters using decimals.
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7cm
(e) 419 cm.
Solution.
"NCERT
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 26

Question 3.
Express as cm using decimals.
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93mm.
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 27
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 28

Question 4.
Expresc as km using decimals.
(a) 8m
(b) 88m
(c) 8888 m
(d) 70 km 5 m.
Solution.
tiwari academy class 6 maths Chapter 8 Decimals 29
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 30

Question 5.
Express as kg using decimals.
(a) 2g
(b) 100g
(c) 3750g
(d) 5kg8g
(e) 26 kg 50g
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 31
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 32
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 33
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 34

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.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 35
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 36
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 37

Question 2.
Rashid spent Rs.35.75 for Maths book and Rs.32.60 for Science book. Find the total amount spent by Rashid.
Solution.
Money spent for Maths book = Rs. 35.75
Money spent for Science book = Rs. 32.60
Total amount spent by Rashid = Rs. 35.75 +Rs.32.60
= Rs. 68.35.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 38

Question 3.
Radhika’s mother gave 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 = Rs. 10.50
Money given by father = Rs. 15.80
Total amount given to Radhika by parents = Rs. 10.50 +Rs.15.80 =Rs. 26.30
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 39

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 her shirt
tiwari academy class 6 maths Chapter 8 Decimals 40

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 walked by Naresh in the morning
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 41
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 42

Question 6.
Sunita travels 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 43
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 46

Question 7.
Ravi purchased 5 kg 400 grice, 2 kg 20 g sugar and 10 kg 850 g flour. Find the total weight of his purchases.
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 47
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 48

Exercise 8.6

Question 1.
Subtract

(a) ₹ 18.25 from ₹ 20.75
(b) ₹ 25from ₹ 20.75
(c) 54 mfrom 250 m
(d) ₹ 36 from ₹ 8.40
(e) 2.051 km from 5.206 km
(f) 0.314 kg from 2.107 kg.
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 49
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 50

Question 2.
Find the value of:
(a) 9.756 – 6.28
(b) 21.05 – 15.27
(c) 18.5 – 6.79
(d) 11.6- 9.847.
Solution.
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 51

Question 3.
Raju bought a book for ₹ 35.65. Did he give? 50 to the shopkeeper. How much money did he get back from the shopkeeper?
Solution.
Book bought for = ₹ 35.65
Money is given to the shopkeeper = ₹ 50
∴ Money got back from the shopkeeper
= ₹ 50 – ?35.65
= ₹ 14.35
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 52

Question 4.
Rani had ₹ 18.50. She bought one ice-cream for ₹ 11.75. How much money does she have now?
Solution.
Money Rani had = ₹ 18.50
Ice-cream bought for = ₹ 11. 75
∴ Money she has now = ₹ 18.50 – ₹ 11. 75
= ₹ 6.75
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 53

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.
Length of cloth Tina had
tiwari academy class 6 maths Chapter 8 Decimals 54

Question 6.
Namita travels 20 km 50 m everyday. 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.
Distance travelled everyday
= 20 km 50 m = 20 km + 50 m
= 20 km +Undefined control sequence \cfrac km
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 55

Question 7.
Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
Solution.
Weight of vegetables bought = 10 kg
Weight of onions = 3 kg 500 g = 3 kg + 500 g
NCERT Solutions for Class 6 Maths Chapter 8 Decimals 56

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