# Decimals Class-6 ML Aggarwal ICSE APC Maths Solutions

Decimals Class-6 ML Aggarwal ICSE APC Mathematics Solutions Chapter-7. We provide step by step Solutions of Exercise / lesson-7 **Fractions**** **ICSE Class-6th ML Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe- 7.1, Exe-7.2, Exe- 7.3, Exe-7.4, Exe- 7.5, Objective Type Questions (includes: Mental Maths, Multiple Choice Questions, HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board **Class-6** Maths.

## Decimals Class-6 ML Aggarwal ICSE APC Mathematics Solutions Chapter-7

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Objective Type Questions

**Exercise – 7.1,** Decimals Class-6 ML Aggarwal ICSE APC Mathematics Solutions

Question 1

Write each of the following decimal numbers in words:

(i) 30.5

(ii) 0.03

(iii) 108.56

(iv) 47.20

(v) 5.008

(vi) 26.039

#### Answer

(i) 30.5 Thirty point five

(ii) 0.03 zero point zero three

(iii) 108.56 One hundred eight point five six

(iv) 47.20 Forty seven point two zero.

(v) 5.008 Five point zero zero eight

(vi) 26.039 Twenty six point zero three nine

Question 2.

Write each of the following decimal numbers in the place value table :

(i) 4.2

(ii) 0.3

(iii) 205.9

(iv) 0.29

(v) 2.08

(vi) 7200.812

(vii) 38.007

#### Answer

Question 3

Write the following decimal numbers in the expanded form :

(i) 123.7

(ii) 43.06

(iii) 509.306

#### Answer

(i) 123.7 = 100 + 20 + 3 +

(ii) 43.06 = 40 + 3 +

(iii) 509.306 = 500 + 9 +

Question 4.

Write each of the following as a decimal number :

#### Answer

Question 5.

Write each of the following as decimals:

(i) Two ones and five tenths

(ii) Two tens and nine tenths

(iii) Six hundred point eight

(iv) Two hundred five anf five hundredths

(v) Seven and fifteen thousandths

#### Answer

Question 6

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

#### Answer

(i) 7102.306

(ii) 211.902

(iii) 3053.015

(iv) 70.03

(v) 5.40

(vi) 719.028

Question 7.

Show the following decimal numbers on the number line:

(i) 0.4

(ii) 1.9

(iii) 1.1

(iv) 2.5

#### Answer

Question 8.

Write the decimal numbers represented by the points A, B, C and D on the given number line:

#### Answer

A = 0.8

B = 1.3

C = 2.2

D = 2.9

Question 9.

Between which two numbers in tenths place on the number line does each of the given number lie?

(i) 0.06

(ii) 0.45

(iii) 0.66

(iv) 0.92

#### Answer

(i) 0 and 0.1

(ii) 0.4 and 0.5

(iii) 0.6 and 0.7

(iv) 0.9 and 1.0

### ML Aggarwal Solutions Decimals Exercise – 7.2 Class-6 ICSE APC Mathematics

Question 1

Write the following decimal fractions as decimal numbers:

#### Answer

Question 2.

Write the following decimal numbers as decimal fractions:

(i) 54.01

(ii) 318.105

(iii) 0.37

(iv) 0.047

(v) 0.03

(vi) 34.5

#### Answer

Question 3.

Write the following decimal numbers as fractions in lowest terms:

(i) 0.8

(ii) 0.04

(iii) 0.125

(iv) 0.225

(vi) 0.066

(vii) 0.092

#### Answer

Question 4.

Convert the following decimal numbers into mixed fractions:

(i) 31.6

(ii) 3.25

(iii) 7.025

(iv) 95.95

#### Answer

Question 5.

Convert the following fractions into decimal numbers:

#### Answer

Question 6.

Convert the following unlike decimal numbers to like decimal numbers :

(i) 17.5, 3.912

(ii) 5.04, 13.1902

(iii) 2.451, 3.7, 28.34

(iv) 3.1,2.678,27.0103

#### Answer

(i) 17.500, 3.912

(ii) 5.0400, 13.1902

(iii) 2.451, 3.700, 28.340

(iv) 3.1000, 2.6780, 27.0103

Question 7.

In each of the following pairs of decimal numbers, state which number is greater ?

(i) 0.3, 0.4

(ii) 1, 0.99

(iii) 1.09, 1.093

(iv) 0.5, 0.05

#### Answer

(i) 0.3, 0.4

Multiply both with 10, we get

3, 4

∴0.4 is greater than 0.3

(ii) 1, 0.99

Multiply both with 100, we get

100, 99

∴ 1 is greater than 0.99

(iii) 1.09, 1.093

Multiply both with 1000, we get

1090, 1093

∴ 1.093 is greater than 1.09

(iv) 0.5, 0.05

Multiply both with 100, we get

50, 5

∴ 0.5 is greater than 0.05

Question 8.

In each of the following pairs of decimal numbers, state which number is smaller:

(i) 45.78, 345.8

(ii) 37.701, 37.71

(iii) 5.907, 5.903

#### Answer

(i) 45.78

(ii) 37.701

(iii) 5.903

Question 9.

Arrange the following decimal numbers in ascending order:

(i) 27.35, 27.305, 2.7, 2.543

(ii) 4.53, 4.07, 29.1, 0.9, 0.709

#### Answer

(i) 2.543, 2.7, 27.305, 27.35

(ii) 0.709, 0.9, 4.07, 4.53, 29.1

Question 10.

Arrange the following decimal numbers in descending order:

(i) 3.303, 33.03, 3.3, 30.33

(ii) 72.5, 2.75, 27.505, 0.275, 2.507

#### Answer

(i) 33.03, 30.33, 3.303, 3.3

(ii) 72.5, 27.505′, 2.75, 2.507, 0.275

**Exercise – 7.3,** Decimals Class-6 ML Aggarwal ICSE APC Mathematics Solutions

Question 1

Add:

(i) 17.5 , 8.8

(ii) 9.999 , 0.03

(iii) 5.87 , 1.03 , 0.1

(iv) 23.71, 9.9, 4.023

(v) 4.5, 16.024, 7.99

(vi) 8.79, 23.001 , 5.41, 0.875

Answer

Question 2

Work out:

(i) 5.82 – 2.65

(ii) 19.01 – 12.234

(iii) 15.4 + 3.015 – 14.237

(iv) 7.4 – 2.19 – 0.456 – 3.5

(v) 19.27 – 3.6 – 8.812 + 0.84

(vi) 6.4 – 2.351 – 1.45 – 0.999

#### Answer

Question 3.

What number added to 0.756 gives 1?

#### Answer

Let the number to be added is = x

According to question,

x + 0.756 = 1

x = 1.000 – 0.756 = 0.244

∴ Number addes is 0.2444.

Question 4.

By how much should 17.45 be decreased to get 7.9702?

#### Answer

One number = 17.45

Outcome = 7.9702

Second number = ?

### Class-6 ML Aggarwal ICSE APC Mathematics Solutions Decimals **Exercise – 7.4**

Question 1

Evaluate the following:

(i) 3.7 × 4.5

(ii) 12.08 × 9.3

(iii) 238.06 × 7.5

(iv) 0.79 × 32.4

(v) 3.6 × 1.4 × 0.7

(vi) 9.01 × 2.5 × 1.6

Answer

Question 2

Work out the following:

(i) 70.756 ÷ 4

(ii) 2.46 ÷ 6

(iii) 3.016 ÷ 8

(iv) 8.64 ÷ 3.6

(v) 72.8 ÷ 0.04

(vi) 0.144 ÷ 0.02

Answer

Question 3

Multiply each of the following numbers by 10, 100 and 1000 orally ;

(i) 4.7

(ii) 3.45

(iii) 23.01

#### Answer

(i) 4.7

4.7 × 10 = 47

4.7 × 100 = 470

4.7 × 1000 = 4700

(ii) 3.45

3.45 × 10 = 34.5

3.45 × 100 = 345

3.45 × 1000 = 3450

Question 4

Divide each of the following numbers by 10, 100 and 1000 (orally):

(i) 4.7

(ii) 3.45

(iii) 23.01

#### Answer

(i) 4.7

4.7 ÷ 10 = 0.47

4.7 ÷ 100 = 0.047

4.7 ÷ 1000 = 0.0047

(ii) 3.45

3.45 ÷ 10 = 0.345

3.45 ÷ 100 = 0.0345

3.45 ÷ 1000 = 0.00345

(iii) 23.01

23.1 ÷ 10 = 2.301

23.1 ÷ 100 = 0.2301

23.1 ÷ 1000 = 0.02301

**Exercise – 7.5,** Class-6 ML Aggarwal ICSE APC Mathematics Solutions Decimals

Question 1

Express as rupees using decimals:

(i) 75 paise

(ii) 1025 paise

(ii) 63 rupees 9 paise

#### Answer

(i) 75 paise = ₹ = ₹0.75

(ii) 1025 paise = ₹ = ₹10.25

(iii) 63 rupees 9 paise = ₹ = ₹63.09

Question 2.

Express as cm using decimals:

(i) 8 mm

(ii) 263 mm

(iii) 13 cm 3 mm

#### Answer

(i) 8 mm = cm = 0.8 cm

(ii) 263 mm = cm = 26.3 cm

(iii) 13 cm 3 mm = 13 cm × cm = 13.3 cm

Question 3.

Express as metres using decimals:

(i) 6 cm

(ii) 528 cm

(iii) 7 m 55 cm

#### Answer

(i) 6 cm = m = 0.06 m

(ii) 528 cm = m = 5.28 m

(iii) 7 m 55 cm = 7 m + 55 cm

= 7 m + m = (7 + .55) m = 7.55 m

Question 4.

Express as km using decimals:

(i) 5 m

(ii) 888 m

(iii) 15 km 88 m

#### Answer

(i) 5 m = km = 0.005 km

(ii) 888 m = km = 0.888 km

(iii) 15 km 88 m = 15 km + 88 m

= 15 km + km = (15 + 0.88) kmsss

= 15.088 km

Question 5.

Express as kg using decimals:

(i) 37 g

(ii) 100 g

(iii) 5 kg 8 g

#### Answer

(i) 37g = kg = 0.037 kg

(ii) 100 g = kg = 0.1 kg

(iii) 5kg 8g = 5kg + 8gm

= 5 kg = kg.

= (5 + .008) kg = 5.008 kg

Question 6.

Anita bought 2 m 70 cm cloth for her shirt and 2 m 85 cm cloth for her trouser. Find the total length of the cloth bought by her.

#### Answer

Cloth bought for her shirt

= 2 m 70 cm = 2 m + 70 cm

= 2 m + m = 2 m + 0.70 m (∵ 1 cm = m)

= (2 m + 0.70) m = 2.70 m

Cloth bought for her trouser

= 2 m 85 cm = 2 m + 85 cm

= 2 m + m = 2 m + 0.85 m (∵ 1 cm = m)

= (2 + 0.85) m = 2.85

∴ Total lengths of cloth bought is 2.70 m + 2.85 m = 5.55 m

Question 7.

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?

#### Answer

Distance travelled by bus

= 15 km 268 m = 15 km + 268 m

= 15 km + km

Question 8.

Rahul bought 4 kg 90 g apples, 2 kg 60 g grapes and 5 kg 300 g mangoes. Find the total weight of all the fruits he bought.

#### Answer

Weight of apples = 4 kg 90 g

= 4 kg + 0.09 kg

= (4 + 0.09) kg = 4.09 kg

Weight of grapes = 2 kg 60 g

= 2kg + (∵ 1g = kg)

= 2 kg + 0.06 kg

= (2 + 0.06) kg = 20.6 kg

Weight of mangoes = 5 kg 300 g

= 5 kg + kg (∵1g = kg)

= 5 kg + 0.3 kg

= (5 + 0.3) kg = 5.3 kg

Total weight of his purchases is

= 4.090 kg + 2.060 kg + 5.300 kg

= 11.450 kg

Question 9.

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

#### Answer

Money Rani had = ₹ 18.75

Ice-cream bought for ₹11.75

∴ Money she has now = ₹ 18.50 – ₹ 11.75 = ₹ 6.75

Question 10.

Tina had 20 m 5 cm long cloth. She cuts 4m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?

#### Answer

Length of cloth Tina had

= 20 m 5 cm = 20 m + 5 cm

Length of cloth cut of 4 m 50 cm

= 4 m + 50 cm

Question 11.

Ruby bought a watermelon weighing 5 kg 300 g. Out of which she gave 2 kg 680 g to her neighbour. What is the weight of the watermelon left with Ruby?

#### Answer

Total weight of watermelon = 5 kg 300 gm

∴Given to neighbour = 2 kg 680 gm

∴ Weight of watermelon left = 5 × 1000 + 300 gm – 2 × 1000 gm + 680 gm

= 5300 gm – 2680 gm = 2620 gm

= = 2 kg 620 gm ⇒ 2.620 kg

Question 12.

The cost of 1 metre of cloth is ₹35.80. What will be cost of 9.8 metres of cloth?

#### Answer

Given : Cost of one metre cloth = ₹35.80

∴ Cost of 9.8 metre cloth is

Cost of 9.8 m cloth = ₹(35.80 × 9.8)

= ₹350.84

Question 13.

Farida bought some bags of cement, each weighing 49.8 kg. If the total weight of all the bags is 1792.8 kg, how many bags did she buy?

#### Answer

Total weight of bag = 1792.8 kg

Weight of cement bag = 49.8 kg

∴ The number of bags she bought

### Objective Type Questions Chapter-7 Decimals for Class-6 ML Aggarwal ICSE APC Mathematics Solutions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) The decimal point in a decimal number is placed between ones digit and ……….. digit.

(ii) The place value of the digit 3 in the decimal number 15.437 is ………

(iii) The decimal number 27.025 has ………. decimal places.

(iv) The decimal number 5.06 is read as five point

(v) If an object is divided into 1000 equal parts, then its 27 parts are represented by ………

(vi) Two decimal numbers having different number of …………. are called unlike decimal numbers.

(vii) 4 tens, 3 ones, 2 tenths, 0 hundredths and 5 thousandths in decimal form is written as ……

(viii)The smallest decimal number upto three decimal places is ……….

#### Answer

(i) The decimal point in a decimal number is placed between ones digit and **tenths** digit.

(ii) The place value of the digit 3 in the decimal number 15.437 is .

(iii) The decimal number 27.025 has **3** decimal places.

(iv) The decimal number 5.06 is read as five point **zero six**.

(v) If an object is divided into 1000 equal parts, then its 27 parts are represented by **0.027**.

(vi) Two decimal numbers having different number of **decimal places** are called unlike decimal numbers.

(vii) 4 tens, 3 ones, 2 tenths, 0 hundredths and 5 thousandths in decimal form is written as **43.205.**

(viii)The smallest decimal number up to three decimal places is **0.001**.

Question 2

State whether the following statements are true (T) or false (F):

(i) Every decimal number can be represented by a point on a number line.

(ii) Fractions with denominator 10, 100, 1000, are called decimal fractions.

(iii) A decimal number having 3 decimal places can be written as a fraction with denominator 1000.

(iv) The value of a decimal number remains the same if any number of extra zeros are written at the end of a decimal number.

(v) If a decimal number is multiplied by 10, then the decimal point moves by one place to the left.

#### Answer

(i) Every decimal number can be represented by a point on a number line. **True**

(ii) Fractions with denominator 10, 100, 1000, are called decimal fractions. **True**

(iii) A decimal number having 3 decimal places can be written as a fraction with denominator 1000. **True**

(iv) The value of a decimal number remains the same if any number of extra zeros are written at the end of a decimal number. **True**

(v) If a decimal number is multiplied by 10, then the decimal point moves by one place to the left. **False**

#### Multiple Choice Question **(MCQ)**

Question 3

Question 3.

Five and seven hundredths is equal to

(a) 5.7

(b) 5.07

(c) 5.70

(d) 0.57

#### Answer

= 5.07 (b)

Question 4.

Sicty three thousandths is equal to

(a) 0.63

(b) 0.603

(c) 0.063

(d) 0.630

#### Answer

0.063 (c)

Question 5.

is equal to :

(a) 3.07

(b) 3.7

(c) 3.70

(d) 3.007

#### Answer

(a)

Question 6.

is equal to

(a) 5.03

(b) 5.3

(c) 5.003

(d) 5.0003

#### Answer

5.003 (c)

Question 7.

The place value of the digit 7 in the decimal number 5.0378 is

#### Answer

(d)

Question 8.

The place value of the digit 0 in the decimal number 13.405 is

#### Answer

Question 9.

The value of is

(a) 5.73

(b) 5.703

(c) 5.073

(d) 0.753

#### Answer

5.703 (b)

Question 10.

The value of is

(a) 1.2

(b) 0.012

(c) 0.12

(d) none of these

#### Answer

Question 11.

The value of is

(a) 5.4

(b) 5.25

(c) 5.04

(d) 5.004

#### Answer

(c)

Question 12.

The decimal number not equivalent to 5.7 is

(a) 5.70

(b) 5.07

(c) 5.700

(d) 5.7000

#### Answer

5.07 (b)

Question 13.

1 g is equal to

(a) 0.1 kg

(b) 0.01 kg

(c) 0.001 kg

(d) 0.0001 kg

#### Answer

0.001 kg (c)

Question 14.

2 km 7 m is equal to

(a) 2.7 km

(b) 2.07 km

(c) 2.007 km

(d) 2.0007 km

#### Answer

(c)

Question 15.

Among 2.34, 2 .43, 2.344 and 2.4, the greatest number is

(a) 2.34

(b) 2.43

(c) 2.344

(d) 2.4

#### Answer

2.34, 2.43, 2.344 and 2.4

Multiply the above number with 100

234, 243, 234.4 and 240

∴ The greater number is 2.43 (b)

Question 16.

5.2 – 3.6 is equal to

(a) 0.16

(b) 2.6

(c) 0.26

(d) 1.6

#### Answer

(d)

Question 17.

A decimal number lying between 2.2 and 2.22 is

(a) 2.12

(b) 2.23

(c) 2.219

(d) 2.3

#### Answer

2.219 (c)

Question 18.

0.023 lies between

(a) 0.2 and 0.3

(b) 0.02 and 0.03

(c) 0.029 and 0.03

(d) 0.026 and 0.024

#### Answer

0.02 and 0.03 (b)

Question 19.

0.7499 lies between

(a) 0.7 and 0.74

(b) 0.759 and 0.799

(c) 0.749 and 0.75

(d) 0.74992 and 0.75

#### Answer

0.749 and 0.75 (c)

Question 20.

Which of the following decimal numbers is the greatest?

(a) 0.182

(b) 0.038

(c) 0.219

(d) 0.291

#### Answer

0.291 (d)

Question 21.

Which of the following decimal numbers is the smallest?

(a) 0.108

(b) 1.08

(c) 0.801

(d) 0.81

#### Answer

0.108 (a)

Question 22.

0.003 × 0.2 is equal to

(a) 0.6

(b) 0.06

(c) 0.006

(d) 0.0006

#### Answer

0.0006 (d)

Question 23.

0.45 + 0.9 is equal to

(a) 50

(b) 5

(c) 0.5

(d) 0.05

#### Answer

0.5 (c)

#### Higher Order Thinking Skills **( HOTS )**

Question 1.

On her birthday, Ayushi is taking her 5 friends to a movie and treats them with cold costs. The cost of a ticket is ₹150 and a cold drink cost ₹28.50. How much Ayushi has to spend?

#### Answer

Number of friends = 5 + 1 Ayushi herself = 6

Cost of 1 ticket = ₹150

Cost of 6 tickets = ₹ 150 × 6 = ₹ 900

Cost of 1 cold drink = ₹28.50

Cost of 6 cold drinks = ₹28.50 × 6 = 171

Ayushi has to spend = ₹900 + ₹171 = ₹ 1071

Question 2.

Write digits in the boxes of the number : to obtain

(i) greatest possible number

(ii) smallest possible number. Repetition of digits in a number is not allowed.

#### Answer

(i) Greatest possible number

(ii) Smallest possible number

**Check Your Progress**

Question 1

Convert the following decimal numbers into fractions (in lowest terms).

(i) 6.015

(ii) 0.876

(iii) 23.375

Answer

Question 2

Write the following fractions as decimals numbers:

#### Answer

Question 3.

Arrange the following decimal numbers in ascending order:

(i) 123.8, 74.205, 74.209, 7.4209

(ii) 85.01, 85.1, 85.001, 85.103

#### Answer

(i) 7.4209, 74.205, 74.209, 123.8

(ii) 85.001, 85.01, 85.1, 85.103

Question 4.

Arrange the following decimal numbers in desending order:

(i) 6.45, 4.65, 6.405, 64.5, 6.54

(ii) 73.5, 35.7, 7.35, 7.53, 7.035

#### Answer

(i) 64.5 > 6.54 > 6.45 > 6.405 > 4.65

(ii) 73.5 > 35.7 > 7.53 > 7.35 > 7.035

Question 5.

If the school bags of Garima and Nakul weigh 5.2 kg and 4.832 kg respectively, find

(i) the total weight.

(ii) the difference in weight of the bags.

#### Answer

Weight of Garima’s bag = 5.2 kg.

Weight of Nakul’s bag = 4.832 kg.

Question 6.

Evaluate the following:

(i) 31.42 – 17.853 -6.43

(ii) 13.01 – 5.428 – 3.703 + 2.99.

#### Answer

(i) 31.42 – 17.853 – 6.43

Question 7

By how much does the sum of 15.453 and 31.647 exceed the sum of 18.47 and 19.506?

Answer

Question 8

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?

Answer

Question 9

Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour (aata). Find the total weight of his purchases.

Answer

Weight of rice purchased

= 5 kg 400 g = 5 kg + 400 g

= 5 kg + kg [∵ 1 g = kg]

= 5 kg + 0.400 kg

= (5 + 0.400) kg = 5.400 kg

Weight of sugar purchased

= 2 kg 20 g = 2 kg + 20 g

= 2 kg = kg [∵ 1 g = kg]

= 2 kg + 0.020 kg = 2.020 kg

Weight of flour purchased

= 10 kg 850 g = 10 kg + 850 g

= 10 kg + kg [∵ 1 g = kg]

= 10 kg + 0.850 kg

= (10 + 0.850) kg = 10.850 kg

∴ Total weight of his purchases is

Question 10

1 kg of pure milk contains 0.263 kg of fat. How much fat is there 15.5 kg of milk?

#### Answer

1 kg of pure milk contains fat = 0.263 kg

∴ 15.5 kg of milk contain fat

Question 11.

The product of two numbers is 15.275. If one number is 4.7, find the other.

#### Answer

The product of two number = 15.275

One number = 4.7

∴ Then other is =

-: End of **Decimals Class-6 ML Aggarwal** Solutions :–

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