Decimals

NCERT Solutions for Class 6 Maths Chapter 8

Decimals are numbers that represent a part of a whole number. They are used to express values smaller than one.

Key Points:

• Place Value:
  
  • The digits to the right of the decimal point represent fractional parts.
  • The first place after the decimal is the tenths place, the second is the hundredths place, and so on.
• Reading and Writing Decimals:
  
  • Decimals are read as whole numbers followed by the decimal point and the place value of the digits after the decimal point.
  • For example, 3.14 is read as “three point one four”.
• Comparing Decimals:
  
  • Compare the whole number parts first. If they are the same, compare the digits after the decimal point, starting from the tenths place.
• Representing Decimals on a Number Line:
  
  • Decimals can be plotted on a number line between whole numbers. The space between two whole numbers is divided into ten equal parts to represent tenths, and so on.
• Addition and Subtraction of Decimals:
  
  • Align the decimal points vertically and then add or subtract as you would with whole numbers.
• Multiplication of Decimals:
  
  • Multiply the numbers as if they were whole numbers, ignoring the decimal points initially.
  • Count the total number of decimal places in the factors and place the decimal point in the product that many places from the right.
• Division of Decimals:
  
  • Convert the divisor to a whole number by multiplying both the divisor and dividend by the same power of 10.
  • Then, divide as you would with whole numbers and place the decimal point in the quotient.

Examples:

• Place value: In 3.14, 3 is the whole number part, 1 is in the tenths place, and 4 is in the hundredths place.
• Comparison: 2.5 is greater than 2.3 because 5 tenths is greater than 3 tenths.
• Addition: 3.25 + 4.17 = 7.42
• Subtraction: 5.6 – 2.3 = 3.3
• Multiplication: 2.5 * 3.2 = 8.00
• Division: 6.4 ÷ 2 = 3.2

NCERT Solutions for Class 6 Maths Chapter 8

Exercise 8.1

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

Ans : 

(a) 0.4 is greater than 0.3 

(b) 0.07 is greater than 0.02 

(c) 3 is greater than 0.8 

(d) 0.5 is greater than 0.05 

(e) 1.23 is greater than 1.2 

(f) 0.19 is greater than 0.099

(g) 1.5 is equal to 1.50 

(h) 1.490 is greater than 1.431 

(i) 3.3 is equal to 3.300 

(j) 5.64 is greater than 5.603

2. Make five more examples and find the greater number from them.

Ans : 

1. 34.52 and 34.25: The greater number is 34.52.
2. 12.09 and 12.9: The greater number is 12.9.
3. 0.789 and 0.79: The greater number is 0.79.
4. 5.001 and 5.01: The greater number is 5.01.
5. 23.456 and 23.46: The greater number is 23.46.

NCERT Solutions for Class 6 Maths Chapter 8

Exercise 8.2

1. Express as rupees using decimals.

(a) 5 paise

(b) 75 paise

(c) 20 paise

(d) 50 rupees 90 paise

(e) 725 paise

Ans : 

(a) 5 paise = 5/100 rupees = Rs. 0.05 

(b) 75 paise = 75/100 rupees = Rs. 0.75 

(c) 20 paise = 20/100 rupees = Rs. 0.20 

(d) 50 rupees 90 paise = 50 + 90/100 rupees = Rs. 50.90

(e) 725 paise = 725/100 rupees = Rs. 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

Ans : 

(a) 15 cm = 15/100 m = 0.15 m 

(b) 6 cm = 6/100 m = 0.06 m 

(c) 2 m 45 cm = 2 m + (45/100) m = 2 + 0.45 m = 2.45 m 

(d) 9 m 7 cm = 9 m + (7/100) m = 9 + 0.07 m = 9.07 m 

(e) 419 cm = 419/100 m = 4.19 m

3. Express as cm using decimals.

(a) 5mm

(b) 60 mm

(c) 164 mm

(d) 9 cm 8 mm

(e) 93 mm

Ans : 

(a) 5 mm = 5/10 cm = 0.5 cm 

(b) 60 mm = 60/10 cm = 6.0 cm 

(c) 164 mm = 164/10 cm = 16.4 cm 

(d) 9 cm 8 mm = 9 cm + (8/10) cm = 9 + 0.8 cm = 9.8 cm 

(e) 93 mm = 93/10 cm = 9.3 cm

4. Express as km using decimals.

(a) 8m

(b) 88 m.

(c) 8888 m

(d) 70 km 5 m

Ans : 

(a) 8 m = 8/1000 km = 0.008 km 

(b) 88 m = 88/1000 km = 0.088 km 

(c) 8888 m = 8888/1000 km = 8.888 km 

(d) 70 km 5 m = 70 km + (5/1000) km = 70 + 0.005 km = 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

Ans : 

(a) 2 g = 2/1000 kg = 0.002 kg 

(b) 100 g = 100/1000 kg = 0.1 kg 

(c) 3750 g = 3750/1000 kg = 3.750 kg 

(d) 5 kg 8 g = 5 kg + (8/1000) kg = 5 + 0.008 kg = 5.008 kg 

(e) 26 kg 50 g = 26 kg + (50/1000) kg = 26 + 0.05 kg = 26.05 kg

NCERT Solutions for Class 6 Maths Chapter 8

Exercise 8.3

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

Ans : 

(a) 0.007 + 8.5 + 30.08 = 38.587 

(b) 15 + 0.632 + 13.8 = 29.432 

(c) 27.076 + 0.55 + 0.004 = 27.63 

(d) 25.65 + 9.005 + 3.7 = 38.355 

(e) 0.75 + 10.425 + 2 = 13.175 

(f) 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.

Ans : 

• Cost of Maths book = Rs. 35.75
• Cost of Science book = Rs. 32.60

Total amount spent = Rs. 35.75 + Rs. 32.60 = Rs. 68.35

Therefore, Rashid spent Rs. 68.35 in total.

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.

Ans : 

Total amount given to Radhika = Amount given by mother + Amount given by father

= Rs. 10.50 + Rs. 15.80

= Rs. 26.30

Therefore, Radhika’s parents gave her a total of Rs. 26.30.

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.

Ans : 

Total length of cloth bought = Length of cloth for shirt + Length of cloth for trouser

• Length of cloth for shirt = 3 m 20 cm = 3.20 m
• Length of cloth for trouser = 2 m 5 cm = 2.05 m

Therefore, Total length of cloth bought = 3.20 m + 2.05 m = 5.25 m

So, Nasreen bought a total of 5.25 meters of cloth.

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?

Ans : 

Total distance walked = Distance walked in the morning + Distance walked in the evenin

• Distance walked in the morning = 2 km 35 m = 2.035 km
• Distance walked in the evening = 1 km 7 m = 1.007 km

Therefore, Total distance walked = 2.035 km + 1.007 km = 3.042 km

So, Naresh walked a total of 3.042 kilometers.

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?

Ans : 

Total distance travelled = Distance by bus + Distance by car + Distance by foot

• Distance by bus = 15 km 268 m = 15.268 km
• Distance by car = 7 km 7 m = 7.007 km
• Distance by foot = 500 m = 0.5 km (since 1000 m = 1 km)

Therefore, Total distance travelled = 15.268 km + 7.007 km + 0.5 km = 22.775 km

So, Sunita’s school is 22.775 km away from her residence.

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.

Ans : 

Total weight of Ravi’s purchases = Weight of rice + Weight of sugar + Weight of flour

• 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

Therefore, Total weight = 5.400 kg + 2.020 kg + 10.850 kg = 18.270 kg

So, the total weight of Ravi’s purchases is 18.270 kg.

NCERT Solutions for Class 6 Maths Chapter 8

Exercise 8.4

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 

Ans : 

(a) 20.75 – 18.25 = 2.50 

(b) 250.00 m – 202.54 m = 47.46 m 

(c) 8.40 – 5.36 = 3.04 

(d) 5.206 km – 2.051 km = 3.155 km 

(e) 2.107 kg – 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

Ans : 

(a) 9.756 – 6.28 = 3.476 

(b) 21.05 – 15.27 = 5.78 

(c) 18.5 – 6.79 = 11.71 (d) 11.6 – 9.847 = 1.753

NCERT Solutions for Class 6 Maths Chapter 8

FAQs

What topics are covered in NCERT solutions for Class 6 Maths Chapter 8?

The NCERT solutions for Class 6 Maths Chapter 8 cover topics related to decimals, including understanding decimals, comparing decimals, and performing arithmetic operations with decimals.

How can NCERT solutions for Class 6 Maths Chapter 8 help me understand decimals better?

The NCERT solutions for Class 6 Maths Chapter 8 provide step-by-step explanations and examples that simplify the concepts of decimals. These solutions help in understanding how to work with decimals effectively.

Are there specific exercises focused on decimals in NCERT solutions for Class 6 Maths Chapter 8?

Yes, Chapter 8 of the Class 6 Maths NCERT book includes exercises specifically focused on decimals. These exercises help students practice and master the concepts related to decimals.

Where can I find NCERT solutions for Class 6 Maths Chapter 8?

NCERT solutions for Class 6 Maths Chapter 8 can be found in educational books and on various online educational platforms. These solutions provide comprehensive coverage of decimals class 6 topics.

What are the key features of decimals covered in NCERT solutions for Class 6 Maths Chapter 8?

The key features of decimals covered in this chapter include understanding place value in decimals, converting fractions to decimals, comparing and ordering decimals, and performing addition, subtraction, multiplication, and division with decimals.

What is the importance of learning decimals in Class 6 Maths?

Learning decimals is crucial in Class 6 Maths as it forms the foundation for more advanced mathematical concepts.