#### Decimals

Exercise 8.1

- Write the following as numbers in the given table:

Solution

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:

Hundreds | Tens | Ones | Tenths |

0 | 3 | 1 | 2 |

- b)In this we see 1 hundreds, 1 tens and 4 tenths.

Hundreds | Tens | Ones | Tenths |

1 | 1 | 0 | 4 |

- Write the following decimals in the place value table.

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

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 |

- 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 =

- b)Two tens and nine tenths =

- c)Fourteen point six = 14.6

- d)One hundred and two ones = 100 + 2 = 102

- e)Six hundred point eight = 600.8

- Write each of the following as decimals:

Solution

- a)There are 5 tenths in the number. So, the decimal representation is 0.5

- b)There are 3 ones and 7 tenths in the number. So, the decimal representation is 3.7

- c)There are 2 hundreds, 6 tens, 5 ones and 1 tenth in the number. So, the decimal representation is 265.1

- d)There are 7 tens, 0 ones and 8 tenths in the number. So, the decimal representation is 70.8

- e)

- f)

- g)For writing in decimal notation, the denominator of the fraction should be 10. So, we make an equivalent fraction as,

Now, writing this fraction in decimal form,

- h)

i)

- j)

- k)

- 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

- 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 is 1 cm.

- Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number?

- a)8 b) 5.1 c) 2.6 d) 6.4 e) 9.1 f) 4.9

Solution

- a)8 = 0 + 8/10

So, it lies between 0 and 1 and is nearer to 1.

- b)1 = 5 + 1/10

So, it lies between 5 and 6 and is nearer to 5.

- c)6 = 2 + 6/10

So, it lies between 2 and 3 and is nearer to 3.

- d)4 = 6 + 4/10

So, it lies between 6 and 7 and is nearer to 6.

- e)1 = 9 + 1/10

So, it lies between 9 and 10 and is nearer to 9.

- f)9 = 4 + 9/10

So, it lies between 4 and 5 and is nearer to 5.

- Show the following numbers on the number line.

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

Solution

- a)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 2
^{nd}part.

- b)9 lies between 1 and 2. There are 9 tenths in it. 1.9 represents the ninth part after 1.

- c)1 lies between 1 and 2. There are 1 tenths in it. 1.1 represents the first part after 1.

- d)5 lies between 2 and 3. There are 5 tenths in it. 2.5 represents the fifth part after 2.

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

Solution

A represents the 8^{th} equal part between 0 and 1. So, A is 0.8.

B represents the 3^{rd} equal part between 1 and 2. So, B is 1.3, C represents the 2^{nd} equal part between 2 and 3 and hence is the number 2.2 and D is 2.9, the 9^{th} equal part between 2 and 3.

- (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)The length of Ramesh’s notebook is 9 cm 5 mm.

- b)The length of a young gram plant is 65 mm.

Exercise 8.2

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

Solution

- a)There are two tenths and 6 hundredths. So, the decimal is 0.26
- b)One whole or ones, 3 tenths and 8 hundredths. Decimal is 1.38
- c)One whole or ones, two tenths and 8 hundredths. Decimal is 1.28

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.

Solution

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

Let us write the decimals in expanded form.

Now, let us complete the table.

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

a) | 0 | 0 | 0 | 2 | 0 | 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.

Solution

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)03 = zero point zero three
- b)20 = one point two zero
- c)56 = one hundred eight point five six.
- d)07 = ten point zero seven.
- e)032 = zero point zero three two
- f)008 = 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

- 0.06 lies between 0 and 0.1
- 0.45 lies between 0.4 and 0.5
- 0.19 lies between 0.1 and 0.2
- 0.66 lies between 0.6 and 0.7
- 0.92 lies between 0.9 and 1
- 0.57 lies between 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

Exercise 8.3

1) Which is greater?

- a)3 or 0.4
- b)07 or 0.02
- c)3 or 0.8
- d)5 or 0.05
- e)23 or 1.2
- f)099 or 0.19
- g)5 or 1.50
- h)431 or 1.490
- i)3 or 3.300
- j)64 or 5.603

Solution

- a)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)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)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)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 I greater.

- f)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)5 or 1.50

Whole number is the same. The tenth part is the same. So, the numbers are equal.

- h)431 or 1.490

The whole number is the 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 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)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.

EXERCISE 8.4

- Express as rupees using decimals.
- a)5 paise
- b)75 paise
- c)20 paise
- d)50 rupees 90 paise
- e)725 paise

Solution

We know that 100 paise = Re 1

Therefore, 1 paise = Re 1/100 = Re 0.01

- 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

1 cm = 1/100 m or 0.01 m

- Express as cm using decimals.
- a) 5 mm (b) 60 mm (c) 164 mm d) 9 cm 8 mm (e) 93 mm

Solution

We know that

1 cm = 1/10 mm or 0.1 mm.

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

Solution

1 m = 1/1000 km or 0.001 km

- 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

1 g = 1/1000 kg = 0.001 kg

EXERCISE 8.5

- 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)007 + 8.5 + 30.08

- b)15 + 0.632 + 13.8

- c)076 + 0.55 + 0.004

- d)65 + 9.005 + 3.7

- e)75 + 10.425 + 2

- f)69 + 25.2 + 38

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

amount spent by Rashid.

Solution

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

**So, Rashid spent Rs. 68.35 for the books.**

- 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.

Solution

Amount given by mother = Rs. 10.50

Amount given by father = Rs. 15.80

Total amount = Rs. 10.50 + 15.80

**The total amount given to Radhika by her parents is 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

Length of the cloth purchased for shirt = 3 m 20 cm

=

Length of the cloth purchased for trouser = 2 m 5 cm

=

Total length of the cloth purchased =

Total length of the cloth purchased = 5.25 m

- 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 in the morning = 2 km 35 m

Distance covered in the evening = 1 km 7 m

Distance he walked in all =

**Distance Naresh walked in all = 3.042 km**

- 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 bus = 15 km 268 m

Distance travelled by car = 7 km 7 m

Distance travelled on foot = 500 m = 0.5 km

Total distance travelled =

**Total distance travelled is 22.775 km**

- 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

Amount of rice = 5 kg 400 g = 5.400 kg

Amount of sugar = 2 kg 20 g = 2.020 kg

Amount of flour = 10 kg 850 g = 10.850 kg

Total purchase =

**Total amount of purchase = 18.270 kg**

EXERCISE 8.6

- Subtract :
- a)Rs 18.25 from Rs 20.75
- b)54 m from 250 m
- c)Rs 5.36 from Rs 8.40
- d)051 km from 5.206 km
- e)314 kg from 2.107 kg

Solution

- a)Rs 18.25 from Rs 20.75

- b)54 m from 250 m

- c)Rs 5.36 from Rs 8.40

- d)051 km from 5.206 km

- e)314 kg from 2.107 kg

- Find the value of :
- a)756 – 6.28
- b)05 – 15.27
- c)5 – 6.79
- d)6 – 9.847

Solution

- a)756 – 6.28

- b)05 – 15.27

- c)5 – 6.79

- d)6 – 9.847
- 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 Raju purchased = Rs. 35.65

Money paid by Raju to the shopkeeper = Rs. 50

Remaining = Rs. 50 – Rs. 35.65

**Hence, Raju gets back Rs. 14.35**

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

Solution

Money with Rani = Rs. 18.50

Amount she spent on an ice-cream = Rs. 11.75

Remaining = 18.50 – 11.75

**Now Rani has Rs. 6.75 left with her.**

- 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 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

**So, 15.55 m cloth was left with her.**

- 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

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 =

**She travelled 9.850 km by auto.**

- 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

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

Weight of potatoes = Weight of the vegetables – weight of onions and tomatoes

= 10 – 5.575

**Weight of potatoes is 4.425 kg.**