# Chapter 8: Decimals

# EXERCISE 8.1

**Write the following as numbers in the given table.**

**Solution:**

Hundreds (100) | Tens (10) | Ones (1) | Tenths (1/10) |

0 | 3 | 1 | 2 |

1 | 1 | 0 | 4 |

**2. Write the following decimals in the place value table.**

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

**Solution:**

S. no. | Hundreds (100) | Tens (10) | Ones (1) | Tenths (1/10) |

(a) | 0 | 1 | 9 | 4 |

(b) | 0 | 0 | 0 | 3 |

(c) | 0 | 1 | 0 | 6 |

(d) | 2 | 0 | 5 | 9 |

**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:**

- 0.7 (b) 20.9 (c) 14.6 (d) 102.0 (e) 600.8

**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 (2/10)**

** (g) 3/2 (h) 2/5**

** (i) 12/5**

**(j) 3(3/5)**

**(k) 4(1/2)**

**Solution:**

- 0.5 (b) 3.7 (c) 265.1 (d) 70.8 (e) 8.8 (f) 4.2 (g) 1.5 (h) 0.4 (i) 2.4 (j) 3.6 (k) 4.5

**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:**

- 6/3, 10/5 (b) 25/5, 10/2 (c) 1, 1 (d) 38/19, 10/5 (e) 137/10, 137/10 (f) 212/10, 106/5

(g) 64/10, 32/5

**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:**

- 0.2cm (b) 3.0 cm (c) 11.6 cm (d) 4.2 cm (e) 16.2 cm (f) 8.3 cm

**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 and 1; 1

(b) 5 and 6; 5

(c) 2 and 3; 3

(d) 6 and 7; 6

(e) 9 and 10; 9

(f) 4 and 5; 5

**8. Show the following numbers on the number line.**

**(a) 0.2 (b) 1.9 (c) 1.1 (d) 2.5**

**Solution: **

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

**Solution:**

A, 0.8 cm; B, 1.3 cm; C, 2.2 cm; D, 2.9 cm.

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:**

- 9.5 cm (b) 6.5 cm

# EXERCISE 8.2

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

**Solution:**

S. no. | Ones | Tenths | Hundredths | Number |

(a) | 0 | 2 | 6 | 0.26 |

(b) | 1 | 3 | 8 | 1.38 |

(c) | 1 | 2 | 8 | 1.28 |

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:**

- 3.25 (b) 102.63 (c) 30.025 (d) 211.902 (e) 12.241

**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:**

Hundreds | Tens | Ones | Tenths | Hundredths | Thousandths | |

(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 |

**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:**

- 29.41 (b) 137.05 (c) 0.764 (d) 23.206 (e) 725.09

**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 zero eight

**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:**

(a) 0 and 0.1 (b) 0.4 and 0.5 (c) 0.1 and 0.2 (d) 0.6 and 0.7 (e) 0.9 and 1.0 (f) 0.5 and 0.6

**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:**

- 3/5 (b) 1/20 (c) 3/4 (d) 9/50 (e) 1/4 (f) 1/8 (g) 33/500

# EXERCISE 8.3

**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) 0.4 (b) 0.07 (c) 3 (d) 0.5 (e) 1.23 (f) 0.19 (g) both are same (h) 1.490 (i) both are same (j) 5.64

# EXERCISE 8.4

**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) ₹ 0.05 (b)₹ 0.75 (c) ₹ 0.20 (d)₹ 50.90 (e) ₹ 7.25

**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**

**Solution:**

- 15 cm

= 15/100 m

= 0.15 m

- 6 cm

= 6/100 m

= 0.06 m

- 2 m 45 cm

= 245/100 m

= 2.45 m

- 9 m 7 cm

= 97/100 m

= 9.07 m

- 419 cm

= 419/100 m

= 4.19 m

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) 0.5 cm (b) 6.0 cm (c) 16.4 cm (d) 9.8 cm (e) 9.3 cm

**4. Express as km using decimals.**

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

**Solution:**

- 0.008 km (b) 0.088 km (c) 8.888 km (d) 70.005 km

**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:**

- 2 g

= 2/1000 kg

=0.002 kg

- 100 g

= 100/1000 kg

=0.1 kg

- 3750 g

= 3750/1000 kg

= 3.750 kg

- 5 kg 8 g

= (5000 + 8)/1000 kg

= 5008/1000 kg

= 5.008 kg

- 26 kg 50 g

= (26000 + 50)/1000 kg

= 26050/1000 kg

= 26.05 kg

# EXERCISE 8.5

**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:**

- 0.007 + 8.5 + 30.08

= 38.587

- 15 + 0.632 + 13.8

= 29.432

- 27.076 + 0.55 + 0.004

= 27.63

- 25.65 + 9.005 + 3.7

= 38.355

- 0.75 + 10.425 + 2

= 13.175

- 280.69 + 25.2 + 38

= 343.89

**2. Rashid spent ****₹35.75 for Maths book and****₹ 32.60 for science book. Find the total amount spent by Rashid.**

**Solution:**

Cost of Maths book = ₹ 35.75

Cost of Science book = ₹ 32.60

Total amount spent by Rashid = cost of Math’s book + cost of science book

= ₹ 35.75 + ₹ 32.60

= ₹ 68.35

Hence the total amount of money spent by Rashid is₹ 68.35

**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 Radhika’s mother = Rs. 10.50

Money given by Radhika’s father = Rs. 15.80

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

= Rs. 26.30

**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:**

We know that 100 cm = 1m

Therefore, 1cm = 1/100 m

3 m 20 cm = 3 m + 20 cm

= 3 m + 20/100 m

= 3 + 0.20 m

= 3.20 m

2 m + 5 cm = 2 m + 5 cm

= 2 m + 5/100 m

= 2 m + 0.05m

= 2.05 m

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

= 5.25m

**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 covered in kilometres by Naresh in the morning = 2 km 35 m = (2 + 35/1000) km = 2.035 km.

Distance covered in kilometres by Naresh in the evening = 1 km 7 m = (1 + 7/1000) km = 1.007 km

Therefore, Total distance walked by him in all = (2.035 + 1.007) km = 3.042 km

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 = 15.268 km

Distance travelled by Sunita by car = 7 km 7 m = 7.007 km

Distance travelled by Sunita by foot = 500 m = 0.500 km

So, the distance from residence to school = 15.268 + 7.007 + 0.500 = 22.775 km

Hence, the distance from her residence to school is 22.775 km.

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.**

**Solution:**

Weight of rice = 5 kg 400 g

Weight of sugar = 2 kg 20 g

Weight of flour = 10 kg 850 g

Total weight = 5 kg 400 g + 2 kg 20 g + 10 kg +850 g

= (5 + 2 + 10) kg + (400 + 20 + 850) g

= 17 kg + 1270 g

= 17kg + 1270/1000 g

= 17 kg + 1.270 kg

= 18.270 kg

# EXERCISE 8.6

**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 – 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 – 2.051) km

= 3.155 km

(e) 0.314 kg from 2.107 kg

= (2.107 – 0.314) kg

= 1.793 kg

**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) 3.476 (b) 5.78 (c) 11.71 (d) 1.753

2. **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?**

**Solution:**

Cost of the book = Rs. 35.65

Money given to shopkeeper = Rs. 50

Money to be returned by shopkeeper = Rs. 50 – Rs. 35.65

Hence, Raju gets Rs. 14.35 back from the shopkeeper.

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

**Solution:**

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.

4. **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:**

The total length of cloth tina had in metres = 20 m 5 cm = 20.05 m

The length of cloth she cuts to make a curtain = 4 m 50 cm = 4.50 m

The length of cloth left with Tina = Total length of cloth – length of cloth she cuts to make a curtain = 20.05 – 4.50 = 15.55m

5. **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; **

We will be using the concept of decimals to solve this.

Total distance travelled by Namita every day = 20 km 50 m

= 20.050 km

The distance travelled by Namita on bus = 10 km 200 m

= 10.200 km

The distance travelled by Namita on auto = Total distance travelled in a day – Distance travelled by bus

= 20.050 – 10.200 = 9.850 km

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