NCERT Solutions Class 6 Mathematics Chapter 8 Decimals

 

Q.1) Write the following as numbers in the given table:

Sol.1) One block divided into 10 equal parts means each part is 1/10 (one-tenth) of a unit. It can be written as 0.1 in decimal notation. One block divided into 100 equal parts means each part is (1/100) one-hundredth of a unit.
a) We see that there are three towers made of 10 blocks representing 3 tens, one block representing ones and two parts of a block representing 2 tenths.
This can be shown on the table as:

Q.2) Write the following decimals in the place value table.
(a) 19.4 (b) 0.3 (c) 10.6 (d) 205.9
Sol.2) Hundreds Tens Ones Tenths
a) 0 1 9 4
b) 0 0 0 3
c) 0 1 0 6
d) 2 0 5 9

Q.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
Sol.3) a) Seven-tenths 7/10 = 0.7
b) Two tens and nine tenths = 20 + 9/10 = 20 + 0.9 = 20.9
c) Fourteen point six = 14.6
d) One hundred and two ones = 100 + 2 = 102
e) Six hundred point eight = 600.8

Q.4) Write each of the following as decimals:
a) 5/10
b) 3 + 7/10
c) 200 + 60 + 50 + 1/10
d) 70 + 8/10
e) 88/10
f) 4(2/10)
g) 3/2
h) 2/5
i) 12/5
j) 3(3/5)
k) 4(1/2)
Sol.4) a) There are 5 tenths in the number, 5/10 = 0.5
So, the decimal representation is 0.5
b) There are 3 ones and 7 tenths in the number, 3 + 7/10 = 3 + 0.7 = 3.7
So, the decimal representation is 3.7
c) There are 2 hundred, 6 tens, 5 ones and 1 tenth in the number, 200 + 60 + 5 + 1/10 = 265 + 0.1 = 265.1
So, the decimal representation is 265.1
d) There are 7 tens, 0 ones and 8 tenths in the number, 70 + 8/10 = 70 + 0.8 = 70.8
So, the decimal representation is 70.8

Q.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
Sol.5) (a) 0.6 = 6/10 = 3/5
(b) 2.5 = 25/10 = 5/2
(c) 1.0 = 1 (d) 3.8 = 38/10 = 19/5
(e) 13.7 = 137/10
(f) 21.2 = 212/10 = 106/5
(g) 6.4 = 64/10 = 32/5

Q.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
Sol.6)

Q.7) Between which two whole numbers on the number line are the given numbers lie?
Which of these whole numbers is nearer the number?

Sol.7) a) 0.8 = 0 + 8/10
So, it lies between 0 and 1 and is nearer to 1.
b) 5.1 = 5 + 1/10
So, it lies between 5 and 6 and is nearer to 5.
c) 2.6 = 2 + 6/10
So, it lies between 2 and 3 and is nearer to 3.
d) 6.4 = 6 + 4/10
So, it lies between 6 and 7 and is nearer to 6.
e) 9.1 = 9 + 1/10
So, it lies between 9 and 10 and is nearer to 9.
f) 4.9 = 4 + 9/10
So, it lies between 4 and 5 and is nearer to 5.

Q.8) Show the following numbers on the number line:
(a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5
Sol.8) a) 0.2 lies between 0 and 1. There are 2 tenths in it. Divide the unit length into 10 equal parts and 0.2 represents the 2nd part.
b) 1.9 lies between 1 and 2. There are 9 tenths in it. 1.9 represents the ninth part after 1.
c) 1.1 lies between 1 and 2. There are 1 tenth in it. 1.1 represents the first part after 1.
d) 2.5 lies between 2 and 3. There are 5 tenths in it. 2.5 represents the fifth part after 2.

Q.9) Write the decimal number represented by the points A, B, C, D on the given number line.

Sol.9) A represents the 8th equal part between 0 and 1. So, A is 0.8.
B represents the 3rd equal part between 1 and 2. So, B is 1.3.
C represents the 2nd equal part between 2 and 3 and
hence is the number 2.2 and D is 2.9, the 9th equal part between 2 and 3.

Q.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.
Sol.10) a) The length of Ramesh’s notebook is 9 𝑐𝑚 5 𝑚𝑚.
9𝑐𝑚 5𝑚𝑚 = 9𝑐𝑚 + 5/10 𝑐𝑚 = 9.5𝑐𝑚(10 𝑚𝑚 = 1 𝑐𝑚)
b) The length of a young gram plant.
65𝑚𝑚 = 65/10 𝑐𝑚 = 6.5 𝑐𝑚

Exercise 8.2

Q.1) Complete the table with the help of these boxes and use decimals to write the number.

Q.2) Write the numbers given in the following place value table in decimal form.

Q.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
Sol.3) Let us write the decimals in expanded form.
a) 0.29 = 0.26 + 0.09 = 2/10 + 9/100
b) 2.08 = 2 + 0.08 = 2 + 8/100
c) 19.60 = 10 + 9 + 0.6 = 1 × 10 + 9 × 1 + 6/10
d) 148.32 = 100 + 40 + 8 + 0.3 + 0.02 = 100 + 4 × 10 + 8 × 1 + 3/10 + 2/100
e) 200.812 = 200 + 0.8 + 0.01 + 0.02 = 2 × 100 + 8/10 + 1/100 + 2/1000
Now, let us complete the table.

Q.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
Sol.5) a) 0.03 = zero point zero three
b) 1.20 = one point two zero
c) 108.56 = one hundred eight point five six.
d) 10.07 = ten point zero seven.
e) 0.032 = zero point zero three two
f) 5.008 = five point zero eight

Q.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
Sol.6) 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
f) 0.57 lies between 0.5 and 0.6

Q.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
Sol.7) a) 0.60 = 60/100 = 6/10 = 3/5
b) 0.05 = 5/100 = 1/20
c) 0.75 = 75/100 = 15/20 = 3/4
d) 0.18 = 18/100 = 9/50
e) 0.25 = 25/100 = 5/20 = 1/4
f) 0.125 = 125/1000 = 25/200 = 5/40 = 1/8
g) 0.066 = 66/1000 = 33/500

Exercise 8.3

Q.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
Sol.1) a) 0.3 = 3/10 and 0.4 = 4/10
The whole number part is the same. It can be seen that the tenth part (3) of 0.3 is less than the tenth part (4) of 0.4.
So, 0.4 is greater.
b) 0.07 = 7/100 and 0.02 = 2/100
The whole number part is the same. It can be seen that the hundredth part (7) of 0.07 is greater than the hundredth part (2) of 0.02.
So, 0.07 is greater.
c) 3 or 0.8/0.8 = 8/100
The whole part 3 is greater than the decimal 0.8
So, 3 is greater
d) 0.5 or 0.05/0.5 = 5/10 and 0.05 = 5/100
The whole part is the same. Tenth part of 0.5 is 5 and the tenth part of 0.05 is 0. So, we see that the tenth part of 0.5 is greater than the tenth part of 0.05. So, 0.5 is greater.
e) 1.23 or 1.2
Whole part is 1 and is the same. The tenth part is also the same. The hundredth part of 1.23 is 3 and the hundredth part of 1.2 is 0. So, we see that 1.23 is greater.
f) 0.099 or 0.19
Whole number part is the same. The tenth part of 0.099 is 0 and that of 0.19 is 1. So, the tenth part of 0.19 is greater than 0.099. Hence, 0.19 is greater.
g) 1.5 or 1.50
Whole number is the same. The tenth part is the same. So, the numbers are equal.
h) 1.431 or 1.490
The whole number is same. The number in the tenth part is also the same. The hundredth part of 1.431 is 3 and that of 1.491 is 9. We see that 3 < 9 and hence 1.431 is lesser than 1.490.
Hence, 1.490 is greater.
i) 3.3 or 3.300
The whole number part and the tenth part are the same. When there are no digits in the hundredths and the thousandths place of the number, we know that the digits are zero.
So, the numbers are the same.
j) 5.64 or 5.603
The whole number and the tenth place digits are the same. As 4 is greater than 0, we know that 5.64 is greater than 5.603.
So, 5.64 is greater.

Q.2) Make five more examples and find the greater number from them.
a) 4.7 or 4.4
b) 7.34 or 7.304
c) 0.043 or 0.00985
d) 10.598 or 10.61
e) 3.23 or 3.25
Sol.2) a) 4.7 or 4.4
Here, the whole part of both the numbers is same.
But the tenth part of 4.7 is greater than that of 4.4.
∴ 4.7 > 4.4

b) 3.23 or 3.25
Here, the whole parts as well as the tenth part of both the numbers are same.
But the hundredth part of 3.25 is greater than that of a 3.23.
Therefore, 3.25 > 3.23.

c) 7.34 or 7.304
Here, the whole parts and the tenth part of both the numbers are same.
But the hundredth part of 7.34 is greater than that of a 7.304.
Therefore, 7.34 > 7.304

d) 0.043 or 0.00985
Here, the whole parts and the tenth part of both the numbers are same.
But the hundredth part of 0.043 is greater than that of a 0.00985.
Therefore, 0.043 > 0.00985

e) 10.598 or 10.61
Here, the whole parts of both the numbers are same.
But the tenth part of 10.61 is greater than that of a 10.598.
Therefore, 10.61 > 10.598

Exercise 8.4

Q.1) Express as rupees using decimals.
(a) 5 paisa (b) 75 paisa (c) 20 paisa
(d) 50 rupees 90 paisa (e) 725 paisa
Sol.1) We know that 100 paisa = Rs.1
Therefore, 1 paisa = 𝑅𝑠. 1/100 = 𝑅𝑠. 0.01
(a) 5 𝑝𝑎𝑖𝑠𝑎 ⇒ 𝑅𝑠. 5/100 = 𝑅𝑠. 0.05
(b) 75 𝑝𝑎𝑖𝑠𝑎 ⇒ 𝑅𝑠. 75/100 = 𝑅𝑠. 0.75
(c) 20 𝑝𝑎𝑖𝑠𝑎 ⇒ 𝑅𝑠. 20/100 = 𝑅𝑠. 0.20
(d) 50 𝑟𝑢𝑝𝑒𝑒𝑠 90 𝑝𝑎𝑖𝑠𝑎 ⇒ 𝑅𝑠. 50 + 𝑅𝑠. 90/100 ⇒ 𝑅𝑠. 50 + 𝑅𝑠. 0.90 = 𝑅𝑠. 50.90
(e) 725 𝑝𝑎𝑖𝑠𝑎 ⇒ 𝑅𝑠. 725/100 = 𝑅𝑠. 7.25

Q.2) Express as metres using decimals.
(a) 15 cm         (b) 6 cm       (c) 2 m 45 cm
(d) 9 m 7 cm    (e) 419 cm
Sol.2)

Q3) Express as cm using decimals.
(a) 5 mm (b) 60 mm (c) 164 mm (d) 9 cm 8 mm
(e) 93 mm
Sol.3) We know that

Q.4) Express as km using decimals.
(a) 8 m (b) 88 m (c) 8888 m (d) 70 km 5 m

Exercise 8.5

Q.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
Sol.1) a) 0.007 + 8.5 + 30.08
                                                   0.007
                                                   8.500
                                              + 30.080
                                                 38.587

b) 15 + 0.632 + 13.8
                                                15.000
                                                  0.632
                                              +13.800
                                                29.432

c) 27.076 + 0.55 + 0.004
                                                27.076
                                                  0.550
                                               + 0.004
                                                27.630

d) 25.65 + 9.005 + 3.7
                                              25.650
                                                9.005
                                             + 3.700
                                              38.355

e) 0.75 + 10.425 + 2
                                               0.750
                                             10.425
                                            + 2.000
                                             13.175

f) 280.69 + 25.2 + 38
                                           280.690
                                             25.200
                                          + 38.000
                                           343.890

Q.2) Rashid spent Rs.35.75 for Maths book and Rs.32.60 for Science book. Find the total amount spent by Rashid.
Sol.2) Amount spent for Maths book = Rs. 35.75
Amount spent for Science book = Rs. 32.60
Total amount spent for the books = 35.75 + 32.60
                      35.75
                  + 32.60
                     68.35
So, Rashid spent Rs. 68.35 for the books.

Q.3) Radhika’s mother gave her Rs.10.50 and her father gave her Rs.15.80, find the total amount given to Radhika by the parents.
Sol.3) Amount given by mother = Rs. 10.50
Amount given by father = Rs. 15.80
Total amount = Rs. 10.50 + 15.80
           10.50
       +  15.80
           26.30
The total amount given to Radhika by her parents is Rs. 26.30

Q.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.
Sol.4) Length of the cloth purchased for shirt = 3 𝑚 20 𝑐𝑚
= 3𝑚 +(20/100)𝑚 = 3𝑚 + 0.20𝑚 = 3.20 𝑚
Length of the cloth purchased for trouser = 2 𝑚 5 𝑐𝑚
= 2𝑚 + (5/100)𝑚 = 2𝑚 + 0.05𝑚 = 2.05𝑚
Total length of the cloth purchased =
                              3.20
                          +  2.05
                              5.25
Total length of the cloth bought by her = 5.25 𝑚

Q.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?
Sol.5) Distance walked in the morning = 2 𝑘𝑚 35 𝑚
2𝑘𝑚 35𝑚 = 2𝑘𝑚 + 35/1000 𝑘𝑚 = 2𝑘𝑚 + 0.035𝑘𝑚 = 2.035 𝑘𝑚
Distance covered in the evening = 1 𝑘𝑚 7𝑚
1 𝑘𝑚 7𝑚 = 1𝑘𝑚 + 7/1000 𝑘𝑚 = 1𝑘𝑚 + 0.007𝑚 = 1.007 𝑘𝑚
Distance he walked all =
                  2.035
               + 1.007
                  3.042
Distance Naresh walked in all = 3.042 𝑘𝑚

Q.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?
Sol.6) Distance travelled by bus = 15 𝑘𝑚 268 𝑚
15𝑘𝑚 268𝑚 = 15𝑘𝑚 + 268/1000 𝑘𝑚 = 15.268 𝑘𝑚
Distance travelled by car = 7𝑘𝑚 7𝑚
7𝑘𝑚 + 7/1000 𝑘𝑚 = 7.007 𝑘𝑚
Distance travelled on foot = 500 𝑚 = 0.5 𝑘𝑚
Total distance travelled =
              15.268
                7.007
             + 0.500
              22.775
Total distance travelled is 22.775 𝑘𝑚

Q.7) Ravi purchased 5 𝑘𝑔 400 𝑔 rice, 2 𝑘𝑔 20 𝑔 sugar and 10 𝑘𝑔 850𝑔 flour. Find the total weight of his purchases.
Sol.7) Amount of rice = 5 kg 400 g = 5.400 kg     (𝟏 𝒈 = 𝟏/𝟏𝟎𝟎𝟎𝒌𝒈 = 𝟎. 𝟎𝟎𝟏 𝒌𝒈)
Amount of sugar = 2 kg 20 g = 2.020 kg
Amount of flour = 10 kg 850 g = 10.850 kg
Total purchase =
                               5.400
                               2.020
                          + 10.850
                             18.270
Total amount of purchase = 18.270 𝑘𝑔

EXERCISE 8.6

Q.1) Subtract :
(a) 𝑅𝑠. 18.25 from 𝑅𝑠. 20.75
(b) 202.54 𝑚 from 250 𝑚
(c) 𝑅𝑠. 5.36 from 𝑅𝑠. 8.40
(d) 2.051 𝑘𝑚 from 5.206 𝑘𝑚
(e) 0.314 𝑘𝑔 from 2.107 𝑘𝑔
Sol.1) (a) 𝑅𝑠. 18.25 from 𝑅𝑠. 20.75
                                   18.25
                                − 20.75
                                    2.50

(b) 202.54 𝑚 from 250 𝑚
                                   250.00 𝑚
                                − 202.54 𝑚
                                     47.46 𝑚

(c) 𝑅𝑠. 5.36 from 𝑅𝑠. 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

Q.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
Sol.2) (a) 9.756 – 6.28
                                   9.756
                                − 6.280
                                   3.476

(b) 21.05 – 15.27
                                   21.05
                                − 15.27
                                     5.78

(c) 18.5 – 6.79
                                  18.50
                                − 6.79
                                  11.71

(d) 11.6 – 9.847
                                 11.600
                                − 9.847
                                  1.753

Q.3) Raju bought a book for Rs.35.65. He gave Rs.50 to the shopkeeper. How much money did he get back from the shopkeeper?
Sol.3) Cost of the book Raju purchased = Rs. 35.65
Money paid by Raju to the shopkeeper = Rs. 50

Remaining = Rs. 50 – Rs. 35.65
                                                       50.00
                                                    − 35.65
                                                       14.35
Hence, Raju gets back 𝑅𝑠. 14.35

Q.4) Rani had Rs.18.50. She bought one ice-cream for Rs.11.75. How much money does she have now?
Sol.4) Money with Rani = Rs. 18.50
Amount she spent on an ice-cream = Rs. 11.75
Remaining = 18.50 – 11.75
                                           18.50
                                        − 11.75
                                             6.75
Now, Rani has 𝑅𝑠. 6.75 left with her.

Q.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?
Sol.5) Length of the cloth Tina had = 20 𝑚 5 𝑐𝑚 = 20.05 𝑚
Length of the cloth she cuts = 4 𝑚 50 𝑐𝑚 = 4.50 𝑚
Length of the cloth left with her = 20.05 𝑚 – 4.50 𝑚
                     20.05
                    − 4.50
                     15.55
So, 15.55 𝑚 cloth was left with her.

Q.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?
Sol.6) Total distance Namita travelled every day is 20 𝑘𝑚 50 𝑚 = 20.050 𝑘𝑚
Distance travelled in bus is 10 𝑘𝑚 200 𝑚 = 10.200 𝑘𝑚
Distance travelled in auto =
                            20.050
                          −10.200
                              9.850
She travelled 9.850 𝑘𝑚 by auto.

Q.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?
Sol.7) Total weight of the vegetables purchased = 10 𝑘𝑔
Weight of onions = 3 𝑘𝑔 500 𝑔 = 3.500 𝑘𝑔
Weight of tomatoes = 2 𝑘𝑔 75 𝑔 = 2.075 𝑘𝑔
Weight of onions and tomatoes = 3.500 + 2.075
                      2.075
                    −3.500
                      5.575
Weight of potatoes = Weight of the vegetables – weight of onions and tomatoes
= 10 – 5.575
                     10.000
                    −5.575
                      4.425
∴ Weight of potatoes = 4.425 𝑘𝑔

 

Question. Amita bought a gift-wrap paper to pack a small gift. She first cut the paper into two equal pieces. Since the pieces still seemed too big, she cut one of those pieces into two equal parts again and used one of them. What decimal fraction of the gift paper did she use?
(a) 0.25
(b) 0.4
(c) 0.3
(d) 0.2

Answer : A

Question. 5/10 + 5/100 - 5/1000 equals
(a) 0.550
(b) 0.555
(c) 0.545
(d) 0.445

Answer : C

Question. How many millilitres of liquid does this dropper contain?

(a) 2.1
(b) 2.4
(c) 2.01
(d) 2.25

Answer : D

Question. Which of the following is the same as 0.25?
(a) 25 Tenths
(b) 1/25
(c) 0.025
(d) 25/100

Answer : D

Question. Mr. Mehta stood on the weighing scales twice, first with and then without his daughter. How much did Mr. Mehta's daughter weigh?

(a) 4.5KG
(b) 5.5KG
(c) 6.5KG
(d) 67.5KG

Answer : B