Class 6 - Maths - Decimals

Exercise 8.1

Question 1:

Write the following as numbers in the given table:

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

Question 2:

Write the following decimals in the place value table:

(a) 19.4                     (b) 0.3                   (c) 10.6                  (d) 205.9

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

(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:

(a) 5/10       (b) 3 + 7/10           (c) 200 + 60 + 5 + 1/10        (d) 70 + 8/10       (e) 88/10

(f) 4           (g) 3/2                  (h) 2/5            (i) 12/5             (j) 3                   (k) 4

(a) 5/10 = 0.5

(b) 3 + 7/10 = 3 + 0.7 = 3.7

(c) 200 + 60 + 5 + 1/10 = 265 + 0.1 = 265.1

(d) 70 + 8/10 = 70 + 0.8 = 70.8

(e) 88/10 = (80 + 8)/10 = 80/10 + 8/10 = 8 + 0.8 = 8.8

(f) 4  = 4 + 2/5 = 4 + 0.4 = 4.4

(g) 3/2 = (3 * 5)/(2 * 5) = 15/10 = 1.5

(h) 2/5 = (2 * 2)/(2 * 5) = 4/10 = 0.4

(i) 12/5 = (12 * 2)/(2 * 5) = 24/10 = 2.4

(j) 3  = 3 + 3/5 = 3 + (3 * 2)/(5 * 2) = 3 + 6/10 = 3 + 0.6 = 3.6

(k) 4  = 4 + 1/2 = 4 + (1 * 5)/(5 * 2) = 4 + 5/10 = 4 + 0.5 = 4.5

Question 5:

Write the following decimals as fraction. Reduce the fractions to lowest terms:

(a) 0.6       (b) 2.5          (c) 1.0              (d) 3.8          (e) 13.7       (f) 21.2            (g) 6.4

(a) 0.6 = 6/10

= 3/5           {6 and 10 are divided by 2}

1. b) 2.5 = 25/10

= 5/2           {25 and 10 are divided by 5}

(c) 1.0 = 10/10

= 1             {10 and 10 are divided by 10}

(d) 3.8 = 38/10

= 19/5        {38 and 10 are divided by 2}

(e) 13.7 = 137/10

(f) 21.2 = 212/10

= 106/5    {212 and 10 are divided by 2}

(g) 6.4 = 64/10

= 32/5         {64 and 10 are divided by 2}

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

(a) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 2 mm = 2/10 cm = 0.2 cm

(b) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 30 mm = 30/10 cm = 3 cm

(c) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 116 mm = 116/10 cm = 11.6 cm

(d) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 2 mm = 2/10 cm = 0.2 cm

Now, 4 cm 2 mm = 4 + 0.2 cm = 4.2 cm

(e) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 162 mm = 162/10 cm = 16.2 cm

(f) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 83 mm = 83/10 cm = 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

From the figure, we can say that

(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

Answer: The numbers are shown on the number line as follows:

Question 9:

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

A:  0 + 8/10 = 0.8

B: 1 + 3/10 = 1 + 0.3 = 1.3

C: 2 + 2/10 = 2 + 0.2 = 2.2

D: 2 + 9/10 = 2 + 0.9 = 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.

(a) 9 cm + 5 mm = 9 cm + 5/10 cm = 9 cm + 0.5 cm = 9.5 cm

So, the length of Ramesh’s notebook is 9.5 cm

(b) 65 mm = 65/10 cm = 6.5 cm

So, the length of a young gram plant is 6.5 cm

Exercise 8.2

Question 1:

Complete the table with the help of these boxes and use decimals to write the number:

Question 2:

Write the numbers given in the following place value table in decimal form:

(a) 0 * 100 + 0 * 10 + 3 * 1 + 2 * (1/10) + 5 * (1/100) + 0 * (1/1000)

= 0 + 0 + 3 + 2/10 + 5/100 + 0

= 3 + 0.2 + 0.05

= 3.25

(b) 1 * 100 + 0 * 10 + 2 * 1 + 6 * (1/10) + 3 * (1/100) + 0 * (1/1000)

= 100 + 0 + 2 + 6/10 + 3/100 + 0

= 102 + 0.6 + 0.03

= 102.63

(c) 0 * 100 + 3 * 10 + 0 * 1 + 0 * (1/10) + 2 * (1/100) + 5 * (1/1000)

= 0 + 30 + 0 + 0 + 2/100 + 5/1000

= 30 + 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 + 9/10 + 0 + 2/1000

= 211 + 0.9 + 0.002

= 102.902

(e) 0 * 100 + 1 * 10 + 2 * 1 + 2 * (1/10) + 4 * (1/100) + 1 * (1/1000)

= 0 + 10 + 2 + 2/10 + 4/100 + 1/1000

= 12 + 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

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

(a) 20 + 9 + 4/10 + 1/100 = 20 + 9 + 0.4 + 0.01 = 29.41

(b) 137 + 5/100 = 137 + 0.05 = 137.05

(c) 7/10 + 6/100 + 4/1000 = 0.7 + 0.06 + 0.004 = 0.764

(d) 23 + 2/10 + 6/1000 = 23 + 0.2 + 0.006 = 23.206

(e) 700 + 20 + 5 + 9/100 = 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

(a) 0.03: Zero point zero three

(b) 1.20: One point two zero

(c) 108.56: One hundred and 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 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

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

(a) 0.60 = 60/100 = 6/10 = 3/5

(b) 0.05 = 5/100 = 1/20

(c) 0.75 = 75/100 = 3/4

(d) 0.18 = 18/100 = 9/50

(e) 0.25 = 25/100 = 1/4

(f) 0.125 = 125/1000 = 5/40 = 1/8

(g) 0.066 = 66/1000 = 33/500

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

Before comparing, we write both terms in like decimals:

(a) 0.3 or 0.4           => 0.3 < 0.4

(b) 0.07 or 0.02      => 0.07 > 0.02

(c) 3 or 0.8               => 3 > 0.8

(d) 0.5 or 0.05         => 0.5 > 0.05

(e) 1.23 or 1.2         => 1.23 > 1.2

(f) 0.099 or 0.19     => 0.099 < 0.19

(g) 1.5 or 1.50         => 1.5 = 1.50

(h) 1.431 or 1.490  => 1.431 < 1.490

(i) 3.3 or 3.300         => 3.3 = 3.300

(j) 5.64 or 5.603       => 5.64 > 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

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

(a) Since 100 paise = Rs 1

So, 1 paise = Rs 1/100

So, 5 paise = Rs (5 *1)/100 = Rs 5/100 = Rs 0.05

(b) Since 100 paise = Rs 1

So, 1 paise = Rs 1/100

So, 75 paise = Rs (75 *1)/100 = Rs 75/100 = Rs 0.75

(c) Since 100 paise = Rs 1

So, 1 paise = Rs 1/100

So, 20 paise = Rs (20 *1)/100 = Rs 20/100 = Rs 0.20

(d) Since 100 paise = Rs 1

So, 1 paise = Rs 1/100

So, 90 paise = Rs (90 *1)/100 = Rs 90/100 = Rs 0.90

Now, 50 rupees 90 paise = 50 + 0.90 = Rs 50.90

(e) Since 100 paise = Rs 1

So, 1 paise = Rs 1/100

So, 725 paise = Rs (725 *1)/100 = Rs 725/100 = Rs 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

(a) Since 100 cm = 1 m

So, 1 cm = 1/100 m

So, 15 cm = (1 * 15)/100 m = 15/100 m = 0.15 m

(b) Since 100 cm = 1 m

So, 1 cm = 1/100 m

So, 6 cm = (1 * 6)/100 m = 6/100 m = 0.06 m

(c) Since 100 cm = 1 m

So, 1 cm = 1/100 m

So, 45 cm = (1 * 45)/100 m = 45/100 m = 0.45 m

Now, 2 m 45 cm = 2 + 0.45 m = 2.45 m

(d) Since 100 cm = 1 m

So, 1 cm = 1/100 m

So, 7 cm = (1 * 7)/100 m = 7/100 m = 0.07 m

Now, 9 m 7 cm = 9 + 0.07 m = 9.07 m

(e) Since 100 cm = 1 m

So, 1 cm = 1/100 m

So, 419 cm = (1 * 419)/100 m = 419/100 m = 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

(a) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 5 mm = (5 * 1)/10 cm = 5/10 cm = 0.5 cm

(b) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 60 mm = (60 * 1)/10 cm = 60/10 cm = 6 cm

(c) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 164 mm = (164 * 1)/10 cm = 164/10 cm = 16.4 cm

(d) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 8 mm = (8 * 1)/10 cm = 8/10 cm = 0.8 cm

Now, 9 cm 8 mm = 9 + 0.8 mm = 9.8 cm

(e) Since 10 mm = 1 cm

So, 1 mm = 1/10 cm

So, 93 mm = (93 * 1)/10 cm = 93/10 cm = 9.3 cm

Question 4:

Express as km using decimals:

(a) 8 m               (b) 88 m           (c) 8888 m          (d) 70 km 5 m

(a) Since 1000 m = 1 km

So, 1 m = 1/1000 km

So, 8 m = (1 * 8)/1000 km = 8/1000 km = 0.008 km

(b) Since 1000 m = 1 km

So, 1 m = 1/1000 km

So, 88 m = (1 * 88)/1000 km = 88/1000 km = 0.088 km

(c) Since 1000 m = 1 km

So, 1 m = 1/1000 km

So, 8888 m = (1 * 8888)/1000 km = 8888/1000 km = 8.888 km

(d) Since 1000 m = 1 km

So, 1 m = 1/1000 km

So, 5 m = (1 * 5)/1000 km = 5/1000 km = 0.005 km

Now, 70 km 5 m = 70 + 0.005 km = 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

(a) Since 1000 g = 1 kg

So, 1 g = 1/1000 kg

So, 2 g = (1 * 2)/1000 kg = 2/1000 kg = 0.002 kg

(b) Since 1000 g = 1 kg

So, 1 g = 1/1000 kg

So, 100 g = (1 * 100)/1000 kg =100/1000 kg = 0.1 kg

(c) Since 1000 g = 1 kg

So, 1 g = 1/1000 kg

So, 3750 g = (1 * 3750)/1000 kg = 3750/1000 kg = 3.750 kg

(d) Since 1000 g = 1 kg

So, 1 g = 1/1000 kg

So, 8 g = (1 * 8)/1000 kg = 8/1000 kg = 0.008 kg

Now, 5 kg 8 g = 5 + 0.008 kg = 5.008 kg

(e) Since 1000 g = 1 kg

So, 1 g = 1/1000 kg

So, 50 g = (1 * 50)/1000 kg = 50/1000 kg = 0.050 kg

Now, 26 kg 50 g = 26 + 0.050 = 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

(a) 0.007                       (b) 15.000              (c)  27.076               (d) 25.650

8.500                           0.632                      0.550                        9.005

+ 30.080                      +13.800                   + 0.004                     + 3.700

Ans:38.587                  Ans:29.432              Ans:27.630               Ans:28.155

(e) 0.750                      (f) 280.69

10.425                          25.20

+   2.000                      +   38.00

Ans:13.175                     Ans:243.89

Question 2:

Rashid spent Rs 35.75 for Maths book and Rs 32.60 for Science book. Find the total amount spent by Rashid.

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

Question 3:

Radhika’s mother have her Rs 10.50 and her father gave her Rs 15.80. Find the total amount given to Radhika by the parents.

Money given by mother = Rs 10.50

Money given by father = Rs 15.80

Total money received by Radha = Rs 10.50 + Rs 15.80 = Rs 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.

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?

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?

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.

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) 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

(a) 20.75                  (b) 250.00              (c) 8.40               (d) 5.206                   (e) 2.107

- 18.25                      - 202.54                 - 5.36                   - 2.051                      - 0.314

02.50                          47.46                    3.04                      2.155                        1.793

= Rs 2.50                    = 47.46 m              = Rs 3.04              = 2.155 km              = 1.793 kg

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

(a) 9.756                  (b) 21.05                   (c) 18.50               (d) 11.600

- 6.280                      - 15.27                   -   6.79                   -  9.847

= 3.476                     = 05.78                =  11.71                    =  1.753

Question 3:

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?

Total amount given to shopkeeper = Rs 50

Cost of book = Rs 35.65

Amount left = Rs 50.00 – Rs 35.65 = Rs14.35

Therefore, Raju got back Rs 14.35 from the shopkeeper.

Question 4:

Rani had Rs 18.50. She bought one ice-cream for Rs 11.75. How much money does she have now?

Total money = Rs 18.50

Cost of Ice-cream = Rs 11.75

Amount left = Rs 18.50 – Rs 11.75 = Rs 6.75

Therefore, Rani has Rs 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?

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?

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?

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.