NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1

Exercise 8.1

Ex 8.1 Class 6 Maths Question 1.
Write the following as numbers in the given table.

Solution:
From the given data, we have

Hundreds (100)	Tens (10)	Ones (1)	Tenths (1/10)
0	3	1	2
1	1	0	4

Ex 8.1 Class 6 Maths Question 2.
Write the following decimals in the place value table.
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205
Solution:
Place value table is given as under:

Ex 8.1 Class 6 Maths 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 x 110 = 0.7
(b) Two tens and nine-tenths = 2 tens + 0 ones + 9 tenths = 20 + 910 = 20.9
(c) Fourteen point six = 14.6
(d) One hundred and two ones
= 1 x 100 + 2 x 1 = 100 + 2 = 102
(e) Six hundred point eight = 600.8

Ex 8.1 Class 6 Maths Question 4.
Write each of the following as decimals:


Solution:

Ex 8.1 Class 6 Maths Question 5.
Write the following decimals as fractions. Reduce the fractions to lowest form.
(a) 0.6
(b) 2.5
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4
Solution:

Ex 8.1 Class 6 Maths 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:
We know that 10 mm = 1 cm.

Ex 8.1 Class 6 Maths 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) 9.1
(f) 4.9
Solution:
(a) 0.8 lies between the whole numbers 0 and 1.
(a) 5.1 lies between the whole numbers 5 and 6.
(b) 2.6 lies between the whole numbers 2 and 3.
(c) 6.4 lies between the whole numbers 6 and 7.
(d) 9.1 lies between the whole numbers 9 and 10.
(e) 4.9 lies between the whole numbers 4 and 5.

Ex 8.1 Class 6 Maths Question 8.
Show the following numbers on the number line.
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5
Solution:

Ex 8.1 Class 6 Maths Question 9.
Write the decimal number represented by the points A, B, C, D on the given number line.

Solution:
Point A represents 0.8
Point B represents 1.3
Point C represents 2.2
Point D represents 2.9

Ex 8.1 Class 6 Maths Question 10.
(a) The length of Ramesh’s notebook is 9 cm 5mm. What will be its length in cm?
(6) The length of a young gram plant is 65 mm. Express its length in cm.
Solution:
(a) Length of the notebook = 9 cm 5 mm

(b) Length of the young gram plant = 65 mm

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.2

Exercise 8.2

Ex 8.2 Class 6 Maths Question 1.
Complete the table with the help of these boxes and use decimals to write the number.

Solution:

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

Explanation:
(a) In this figure,
If small block out of 100 are shaded
∴ Decimal representation = 0.26

(b ) 100 small blocks + 38 small blocks are shaded

∴ Decimal representation = 1.38

(c) 100 small blocks + 28 small blocks are shaded

∴ Decimal representation = 1.28

Ex 8.2 Class 6 Maths Question 2.
Write the numbers given in the following place value table in decimal form:

Solution:
(a) 0 Hundreds + 0 Tens + 3 Ones + 2 Tenths + 5 Hundredths + 0 Thousandths

= 3 + 0.2 + 0.05 + 0.000 = 3.250 = 3.25

(b) 1 Hundreds + 0 Tens + 2 Ones + 6 Tenths + 3 Hundredths + 0 Thousandths

= 102.630 = 102.63

(c) 0 Hundreds + 3 Tens + 0 Ones + 0 Tenths + 2 Hundredths + 5 Thousandths
= 0 x 100 + 3 x 10 + 0 x 1 + 0 x 110 + 2 x 1100 + 5 x 11000
= 0 + 30 + 0 + 0.0 + 0.02 + 0.005
= 30.025

(d) 2 Hundreds + 1 Tens + 1 Ones + 9 Tenths + 0 Hundredths + 2 Thousandths
= 2 x 100 + 1 x 10 + 2 x 110 + 0 x 1100 + 2 x 1100
= 200 + 10 + 1 + 0.9 + 0.00 + 0.002
= 211 + 0.902 = 211.902

(e) 0 Hundreds + 1 Tens + 2 Ones + 2 Tenths + 4 Hundredths + 1 Thousandths
= 0 x 100 + 1 x 10 + 2 x 1 + 2 x 110 + 4 x 1100 + 1 x 11000
= 0 + 10 + 2 + 210 + 4100 + 11000
= 12 + 0.2 + 0.04 + 0.001 = 12.241

Ex 8.2 Class 6 Maths 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:
(a) 0.29 = 0 + 0.2 + 0.09 = 0 Ones + 2 Tenths + 9 Hundredths
(b) 2.08 = 2 + 0.0 + 0.08
= 2 Ones + 0 Tenths + 8 Hundredths
(c) 19.60 = 10 + 9 + 0.6 + 0.00
= 1 Tens + 9 Ones + 6 Tenths + 0 Hundredths
(d) 148.32 = 100 + 40 + 8 + 0.3 + 0.02
= 1 Hundred + 4 Tens + 8 Ones + 3 Tenths + 2 Hundredths
(e) 200.812 = 200 + 0.8 + 0.01 + 0.002
= 2 Hundreds + 8 Tenths + 1 Hundredth + 2 Thousandths
The above information, we can gives in place value Table:

	Hund­reds (100)	Tens (10)	Ones (1)	Ten­ths (1/10)	Hund­redths (1/100)	Thous­andths (1/1000)
(a)	0	0	0	2	9	0
(b)	0	0	2	0	8	0
(c)	0	1	9	6	0	0
(d)	1	4	8	3	2	0
(e)	2	0	0	8	1	2

Ex 8.2 Class 6 Maths Question 4.
Write each of the following as decimals.

Solution:

Ex 8.2 Class 6 Maths 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) 0.03 = Zero point zero three
(b) 1.20 = One point two zero
(c) 108.56 = One hundred eight point fifty-six
(d) 10.07 = Ten point zero seven
(e) 0.032 = Zero point zero three two
(f) 5.008 = Five point zero zero eight

Ex 8.2 Class 6 Maths Question 6.
Between which two numbers in tenths place on the number line does each of the given numbers lie?
(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57
Solution:
(a) 0.06 lies between 0 and 0.1
(b) 0.45 lies between 0.4 and 0.5
(c) 0.19 lies between 0.1 and 0.2
(d) 0.66 lies between 0.6 and 0.7
(e) 0.92 lies between 0.9 and 1.0
(f) 0.57 lies between 0.5 and 0.6

Ex 8.2 Class 6 Maths Question 7.
Write as fraction in lowest terms.
(a) 0.60
(b) 0.05
(c) 0.75
(e) 0.25
(f) 0 .125
(g) 0.066

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.3

Exercise 8.3

Ex 8.3 Class 6 Maths 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

∴ 0.4 is greater than 0.3

(b) 0.07 or 0.02

∴ 0.07 is greater than 0.02.

(c) 3 or 0.8
3 is greater than 0 and 0 > 0.8
∴ 3 is greater than 0.8.

(d) 0.5 or 0.05

∴ 0.5 is greater than 0.05.

(e) 1.23 or 1.2

∴ 1.23 is greater than 1.2

(f) 0.099 or 0.19

∴ 0.19 is greater than 0.099.

(g) 1.5 or 1.50

∴ 1.5 is greater than 1.50.

(h) 1.431 or 1.490

∴ 1.490 is greater than 1.431.

(i) 3.3 or 3.300

∴ 3.3 is greater than 3.300.

(j) 5.64 or 5.603

∴ 5.64 is greater than 5.603.

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.4

Exercise 8.4

Ex 8.4 Class 6 Maths 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:

= ₹7.25
So, 725 paise = ₹7.25

Ex 8.4 Class 6 Maths Question 2.
Express as metres using decimals,
(a) 15cm
(b) 6cm
(c) 2m 45cm
(d) 9m 7cm
(e) 419 cm
Solution:

Ex 8.4 Class 6 Maths 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:

Ex 8.4 Class 6 Maths Question 4.
Express as km using decimals.
(a) 8 m
(b) 88 m
(c) 8888 m
(d) 70km 5m
Solution:


Ex 8.4 Class 6 Maths 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:

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.5

Exercise 8.5

Ex 8.5 Class 6 Maths 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:
(a) 0.007 + 8.5 + 30.08
= 0.007 + 8.500 + 30.080 (making like decimals)
= 38.587

(b) 15 + 0.632 + 13.8
= 15.000 + 0.632 + 13.800 (making like decimals)
= 29.432

(c) 27.076 + 0.55 + 0.004
= 27.076 + 0.550 + 0.004 (making like decimals)
= 27.630

(d) 25.65 + 9.005 + 3.7
= 25.650 + 9.005 + 3.700 (making like decimals)
= 38.355

(e) 0.75 + 10.425 + 2
= 0.750 + 10.425 + 2.000 (making like decimals)
= 13.175

(f) 280.69 + 25.2 + 38
= 280.69 + 25.20 + 38.00 (making like decimals)
= 343.89

Ex 8.5 Class 6 Maths Question 2.
Rashid spent ₹35.75 for Maths book and ₹32.60 for Science book. Find the total amount spent by Rashid.
Solution:
Money spent by Rashid for Maths book = ₹35.75
Money spent by Rashid for Science book = ₹32.60
∴ Total money spent by Rashid on both books = ₹35.75 + ₹32.60 = ₹68.35

Ex 8.5 Class 6 Maths Question 3.
Radhika’s mother gave her ₹10.50 and her father gave her ₹15.80, find the total amount given to Radhika by her parents.
Solution:
Money given by Radhika’s mother = ₹10.50
Money given by her father = ₹15.80
∴ Total money given to her by her parents
= ₹10.50 + ₹15.80 = ₹26.30

Ex 8.5 Class 6 Maths 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:
Length of cloth bought by Nasreen for her shirt = 3 m 20 cm = 3.20 m
Length of cloth brought by her for her trouser = 2 m 5 cm = 2.05 m
Total length of cloth bought by her = 3.20 m + 2.05 m = 5.25 m

Ex 8.5 Class 6 Maths 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 = 2 km 35 m = (2 + 351000) km = 2.035 km.
Distance walked by him in the evening = 1 km 7 m = (1 + 71000) km = 1.007 km 1000)
∴ Total distance walked by him in all
= (2.035 + 1.007) km
= 3.042 km

Ex 8.5 Class 6 Maths Question 6.
Sunita travelled 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:
Distance travelled by Sunita by bus
= 15 km 268 m = ( 15 + 2681000) = 15.268 km
Distance travelled by her by car
= 7 km 7 m = (7 + 71000) km
= 7.007km

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.6

Exercise 8.6

Ex 8.6 Class 6 Maths Question 1.
Subtract:
(a) ₹18.25 from ₹20.75
(b) 202.54 m from 250 m
(c) ₹5.36 from ₹8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg
Solution:
(a) ₹18.25 from 20.75
= 20.75 – 18.25
= 2.50

(b) 202.54 m from 250 m
= 250 m – 202.54 m
= 250.00 m – 202.54 m
= 47.46 m

(c) ₹5.36 from ₹8.40
= ₹8.40 – ₹5.36
= ₹3.04

(d) 2.051 km from 5.206 km
= 5.206 km – 2.051 km
= 3.155 km

(e) 0.314 kg from 2.107 kg
= 2.107 kg – 0.314 kg
= 1.793 kg

Ex 8.6 Class 6 Maths 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:
(a) We have 9.756 – 6.25
= 9.756 – 6.250
= 3.506

(b) We have 21.05 – 15.27
= 5.78

(c) We have 18.5 – 6.79
= 18.50 – 6.79
= 11.71

(d) 11.6 – 9.847
= 11.600 – 9.847
= 1.753

Ex 8.6 Class 6 Maths Question 3.
Raju bought a book for ₹35.65. He gave ₹50 to the shopkeeper. How much money did he get back from the shopkeeper?
Solution:
Cost of book = ₹35.65
Money paid by him to the shopkeeper = ₹50
∴ Money got back by him
= ₹50 – ₹35.65
= ₹50.00 – ₹35.65
= ₹14.35

Ex 8.6 Class 6 Maths 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
She bought ice-cream for ₹11.75
∴ Money left with Rani = ₹ 18.50 – ₹11.75 = ₹6.75

Ex 8.6 Class 6 Maths 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 had by Tina = 20 m 5 cm = 20.05 m
Length of cloth cut by her = 4 m 50 cm
= 4.50 m
∴ Length of cloth left with her = 20.05 m -4.50 m
= 15.55 m

Ex 8.6 Class 6 Maths 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:
Distance travelled by Namita daily = 20 km 50 m or 20.050 km
Distance travelled by her by bus = 10 km 200 m or 10.200 km
∴ Distance travelled by her by auto = (20.050 – 10.200) km = 9.850 km

Ex 8.6 Class 6 Maths 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 by Aakash = 10 kg
Weight of onions bought by him = 3 kg 500 g
= 3.500 kg
and weight of tomatoes bought by him = 2 kg 75 g = 2.075 kg
∴ Weight of potatoes = Weight of vegetable – (weight of onions + weight of tomatoes)
= 10.000 – (3.500 + 2.075)
= 10.000 – 5.575 = 4.425 kg