# NCERT Class 6 Maths Chapter 8 ‘Decimals’: Notes and Solutions (Free PDF)

In this chapter, students will understand everything related to Decimals. The chapter is very important as it lays the foundation for understanding the Decimals for complex calculations. Students will learn concepts like representing decimals on a number line, decimals as fractions, tenths, and hundredths, comparing decimals, using decimals for length, weight, and money, the addition of numbers with decimals and subtraction of decimals with numbers. In Chapter 8 of Class 6 Maths, students will learn the concept of decimals which will be useful for them in all their future higher study lessons. Read through for CBSE NCERT Class 6 Maths Chapter 8 Decimals Notes, Exercise, and Important Questions.

## NCERT Class 6 Maths Chapter 8 Decimals Notes – Free PDF Download

Below we have given topic-wise notes for the CBSE NCERT Class 6 Maths Chapter 8 Decimals. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall.

### Topic 1: Representing Decimals on Number Line

We have learned how to represent fractions on a number line. Now let us understand how to represent decimals on a number line with the help of the following example.

For eg, let us represent 0.6 on the number line. We know 0.6 is greater than 0 but lesser than 1. Let us mark 10 points between 0 and 1 at equal distances, so, 0.6 will be placed at:

### Topic 2: Fractions as Decimals

To convert fractions into decimals, the best way is to convert the denominator into 10 or a multiple of 10 because we know:

Here, 0.1 is called the tenth part of the decimal and 0.01 is called the hundredth part of the decimal.

### Topic 3: Comparing Decimals

To compare the decimal values, we start our comparison in the following steps:

1. Compare the whole part: To compare the decimal values, we start comparing from left to right. So, we first compare the whole part, i.e. the numbers to the left of the decimal point.
2. Compare the tenth part of the decimal: As discussed above, after we compare the whole part of a decimal, we compare its tenth part.
3. Compare the hundredth part: If the tenth part of the two given numbers are also equal, then we move on to comparing the hundredth part.

## Important Questions in NCERT Class 6 Maths Chapter 8: Free PDF Download

Below we have provided some important exercise questions and their solutions from Chapter 8 of CBSE NCERT Maths for Class 6.

### Exercise 8.1

Q 1.  Write the following decimals in the place value table.

1. 19.4
2. 0.3
3. 10.6
4. 205.9

Ans. The Decimals in the place value table are given below.

Q 2.  Write each of the following as decimals :

1. Seven-tenths
2. Two tens and nine-tenths
3. Fourteen point six
4. One hundred and two ones
5. Six hundred point eight

Ans. The decimal forms of each of the given numbers are:

1. Two tens = 20
1. 14.6
2. One hundred and two ones = 100 + 2 = 102
3. 600.8

Q 3. Express the following as cm using decimals.

1. 116 mm
2. 4 cm 2 mm
3. 162 mm

Ans. The conversions of the given values are:

1. We know that 1 cm = 10 mm

So, 1 mm = 1/10 cm

∴ 116 mm = 116/10 = 11.6 cm

1. 4 cm 2 mm = 4 cm + 2/10 cm = 4.2 cm
2. 162 mm ⇒ 162/10 cm = 16.2 cm

Q 4. Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Ans. The natural numbers from 2 to 12 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Hence, the total numbers are 11.

Prime numbers from natural numbers 2 to 12 are 2, 3, 5, 7, 11 = 5 prime numbers.

So, the fraction of prime numbers is 5/11

### Exercise 8.2

Q 1.  Write each of the following as decimals.

Ans. The decimal value of each of the given problems is:

Q 2.  Write each of the following decimals in words.

1. 0.03
2. 1.20
3. 108.56

Ans. The given decimals will be expressed in words as follows:

1. Zero point zero three
2. One point two zero
3. One hundred eight point five six

Q 3.  Between which two numbers in tenth place on the number line does each of the given number lie?

1. 0.06
2. 0.45
3. 0.19

Ans. Let us see the answers below:

1. 0.06 lies between 0.0 and 0.1 in the tenth place of the number line.
2. 0.45 lies between 0.4 and 0.5 in the tenth place of the number line.
3. 0.06 lies between 0.1 and 0.2 in the tenth place of the number line.

### Exercise 8.3

Q 1. Which is greater?

1. 0.3 or 0.4
2. 0.07 or 0.02
3. 3 or 0.8
4. 0.5 or 0.05
5. 1.23 or 1.2
6. 0.099 or 0.19
7. 1.5 or 1.50
8. 1.431 or 1.490
9. 3.3 or 3.300
10. 5.64 or 5.603

Ans. As the rule mentioned above, we will start comparing the given numbers from the left side of the decimals. Hence, the answers are:  ><

1. Among 0.3 and 0.4, in the tenth place, 0.4 is greater.

So, 0.3 < 0.4

We will solve the rest of the questions in a similar manner.

1. 0.07 > 0.02
2. 3 > 0.08
3. 0.5 > 0.05
4. 1.23 > 1.2
5. 0.099 < 0.19
6. 1.5 = 1.50
7. 1.431 < 1.490
8. 3.3 = 3.300
9. 5.64 > 5.603

### Exercise 8.4

Q 1. Express as rupees using decimals.

1. 5 paise
2. 75 paise
3. 20 paise
4. 50 rupees 90 paise

Ans. We know that 1 Rs = 100 Paisa

So, 1 Paisa = 1/100 Rs

### Exercise 8.5

Q 1.  Rashid spent ₹ 35.75 for the Maths book and ₹ 32.60 for the Science book. Find the total

amount spent by Rashid.

Ans. The total amount paid by Rashid = ₹ 35.75 + ₹ 32.60 = ₹ 68.35

Q 2.  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. The total amount given to Radhika is = ₹ 10.50 + ₹ 115.80 = ₹ 26.30

### Exercise 8.6

Q 1.  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?

Ans. We know that 1 m = 100 cm, so, 1 cm = 1/100 m.

Total length of cloth = 20 m 5 cm = 20.05 m

Piece of cloth taken by Tina for making curtain = 4 m 50 cm = 4.5 m

Cloth left with Tina = 20.05 m – 4.5 m = 15.55 m

Also See:

## FAQs

Q.1. What are Decimals?

Ans: A decimal is used to define the uncertain value or the value in parts after the whole value.

Q.2. How can we convert fractions into Decimals?

Ans: To convert fractions into decimals, the best way is to convert the denominator into 10 or a multiple of 10.

Q.3. Why are Decimals used?

Ans: Decimals are used to define some measurements where precision is required and merely whole numbers cannot define the exact measurement. This is useful when we are dealing with very small quantities of physical properties.

This was all about CBSE NCERT Class 6 Maths Chapter 8 Decimals Notes and Important Exercise Questions and Answers PDF Free Download. Follow the CBSE Class 6 Maths Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 6 Maths.