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Important Questions for CBSE Class 6 Maths Chapter 8 - Decimals

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CBSE Class 6 Maths Important Questions Chapter 8 - Decimals - Free PDF Download

Every day, we use decimals when dealing with money, weight, length, etc. So Decimals and their applications are very important for students to understand. Vedantu provides free PDF solutions on Class 6 Maths Chapter 8 Important Questions according to NCERT curriculum. These solutions are prepared by experts who have a vast knowledge of Decimal and related topics. These solutions are carefully designed in such a way it provides students with a step by step explanation of the solution so that every doubt of students is cleared when they refer to the solution.

 

Free PDF download of Important Questions with solutions for CBSE Class 6 Maths Chapter 8 - Decimals prepared by expert Mathematics teachers from the latest edition of CBSE(NCERT) books. Register online for Maths tuition on Vedantu.com to score more marks in your examination. 

 

You can also register Online for NCERT Class 6 Science tuition on Vedantu.com to score more marks in CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for the better solutions ,can download Class 6 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations. 

 

Download CBSE Class 6 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 6 Maths Important Questions for other chapters:

CBSE Class 6 Maths Important Questions

Sl.No

Chapter No

Chapter Name

1

Chapter 1

Knowing Our Numbers

2

Chapter 2

Whole Numbers

3

Chapter 3

Playing with Numbers

4

Chapter 4

Basic Geometrical Ideas

5

Chapter 5

Understanding Elementary Shapes

6

Chapter 6

Integers

7

Chapter 7

Fractions

8

Chapter 8

Decimals

9

Chapter 9

Data Handling

10

Chapter 10

Mensuration

11

Chapter 11

Algebra

12

Chapter 12

Ratio and Proportion

13

Chapter 13

Symmetry

14

Chapter 14

Practical Geometry


The PDF also includes a solution for Class 6 Maths Chapter 8 Extra Questions on Decimals. These extra questions with solutions are prepared to provide additional practice problems for students to test their subject knowledge and to prepare for their exams.

 

The important topics covered in Decimals chapter are as follows:

  • Definition of decimals with examples

  • Representing Decimals on a number line

  • Fractional notation of Decimals

  • Comparing decimals

  • Decimals in length and weight measurement

  • Addition and subtraction of decimals


Overview of Class 6 Maths Chapter 8 Decimals Important Questions

The concept of decimals and fractions are dealt with in Class 6 Maths Chapter 8. Students will be introduced to some new and advanced concepts in this chapter. They will understand the definition of the term decimal and learn the examples. They will also understand how to represent decimal numbers on the number line. Apart from that, the chapter also discloses the fractional notation of decimals. The comparison of decimals, measurements using decimals, and addition and subtraction using decimals, are also some of the main topics to be covered in this chapter. After completing the chapter, students can download important questions for Class 6 Maths Chapter 8 Decimals from Vedantu and start practising.

 

To score good marks in exams, it is vital for students to understand every single chapter in their Class 6 Maths textbook. The chapter on Decimals is a very significant one since it has weightage in the examinations. With the important questions in this chapter, students will be able to complete their syllabus in time and that too with detailed knowledge. These questions have solutions as well that students can practise and in turn improve their answering skills. The learned Maths experts at Vedantu have formulated these questions according to the CBSE guidelines. Following the questions will enable students to tap into the best study resources and perform well during exams.

Study Important Question for Class 6 Mathematics Chapter 8 – Decimals

1 Mark Questions

1. Write in decimal form: $400 + 60 + 7 + \dfrac{2}{{10}} + \dfrac{5}{{100}} + \dfrac{5}{{1000}}$

Ans: Let’s use basic arithmetic operations:

$= 400 + 60 + 7 + \dfrac{2}{{10}} + \dfrac{5}{{100}} + \dfrac{5}{{1000}}$

$= 467 + \dfrac{{200 + 50 + 5}}{{1000}}$

$= 467 + 0.255$

$= 467.255$


2. Express the term $4\;{\text{m}}$ in ${\text{km}}$ using decimals.

Ans:

$\because 1\;{\text{km}}\,{\text{ = 1000}}\;{\text{m}}$

$\therefore 4\;{\text{m}} = \dfrac{4}{{1000}}\;{\text{km}} = 0.004\;{\text{km}}$


3. \[\dfrac{{\text{9}}}{{{\text{1000}}}}\], in decimal form can be written as:

Ans: $\dfrac{9}{{1000}} = 0.009$


4. The correct expanded form of $3.07$ is

(a) $(3 \times 10) + \left( {7 \times \dfrac{1}{{10}}} \right)$

(b) $(3 \times 1) + \left( {7 \times \dfrac{1}{{10}}} \right)$

(c) $(3 \times 1) + \left( {7 \times \dfrac{1}{{100}}} \right)$

(d) None of these 

Ans:  (C)

Since,

$3.07 = 3 + 0.07$

$\Rightarrow (3 \times 1) + \left( {7 \times \dfrac{1}{{100}}} \right)$


5. Fill in the blanks, $2 - 0.7 = \_\_\_$                    

Ans:

$2.0-0.7=1.3$


2 Mark Questions

1. Express $17\dfrac{{13}}{{1000}}$ as decimals

Ans: $\Rightarrow 17\dfrac{{13}}{{1000}}$

$= \dfrac{{17 \times 1000 + 13}}{{1000}}$

$= \dfrac{{17000 + 13}}{{1000}}$ 

$= \dfrac{{17013}}{{1000}}$

$= 17.013$


2. Convert  \[6.3,{\text{ }}8.19,{\text{ }}0.276{\text{ }}and{\text{ }}74\]  into like decimals

Ans: So, we need to convert the given number \[6.3,{\text{ }}8.19,{\text{ }}0.276,{\text{ }}74\] into decimals. Since, we know that decimals that have the same number of decimal places are called decimals.

Therefore, the like decimals will be:

$ \Rightarrow 6.300,\;8.190,\;0.276,\;74.000$


3. Compare 34.7 and 34.68

Ans: In the given question we need to compare two numbers. So for comparing two numbers, we always need to compare each of the digit places. 

Here, it can be seen that before the decimal places both have the same digits. So now we will compare the digits after the decimals. 

Therefore, on comparing it, we get:

 $34.7 > 34.68$


4. Add and express in kilograms using decimals: $3\;{\text{kg}}$ and $448\;{\text{g}}$.

Ans: $3\;{\text{kg}}\;{\text{and}}\;448\;{\text{g}}$

$ \Rightarrow 3\;{\text{kg}} + 448\;{\text{g}}$

$\because 1\;{\text{g = }}\dfrac{1}{{1000\;{\text{kg}}}}$

$\therefore 3\,{\text{kg}} + \dfrac{{448}}{{1000}}\;{\text{kg}}$

$ \Rightarrow 3\;{\text{kg}} + 0.448\;{\text{kg}}$

$ \Rightarrow 3.448\;{\text{kg}}$


5. Express $4\;{\text{g}}$ in kilograms using decimals.

Ans: $\because 1\;{\text{g}}\,{\text{ = }}\dfrac{1}{{1000\;{\text{kg}}}}$

$ \Rightarrow 4\;{\text{g}} = \dfrac{4}{{1000}}\;{\text{kg}} = 0.004\;{\text{kg}}$


6. Express in kilometres using decimals $8\;{\text{km}}\;56\;{\text{m}}$.

Ans: $8\;{\text{km}}\;56\;{\text{m}}$

$\because 1\;{\text{m}}\,{\text{ = }}\dfrac{1}{{1000\;{\text{km}}}}$

$ \Rightarrow 8\;{\text{km}} + 56\;{\text{m}}$

$ \Rightarrow 8\;{\text{km}} + \dfrac{{56}}{{1000}}\;{\text{km}}$

$ \Rightarrow 8\;{\text{km}} + 0.056\;{\text{km}}\;{\text{ = }}\;8.056\;{\text{km}}$


3 Mark Questions 

1. Write the following in ascending order \[3.83,{\text{ }}5.07,{\text{ }}0.8,{\text{ }}0.365{\text{ and }}6.4\] .

Ans: Converting into like terms

\[3.830,{\text{ }}5.070,{\text{ }}0.800,{\text{ }}0.365,{\text{ }}6.400\]

So, the ascending order is:

\[0.365,{\text{ }}0.800,{\text{ }}3.830,{\text{ }}5.070,{\text{ }}6.400\]


2. Convert into decimal fraction $\dfrac{{39}}{4}$

Ans: By performing division:

$\begin{matrix} &4\overset{{9.75}}{\overline{)\;39\;}}\\ &-36\\ &\qquad\overline{\;30\;}\\ &\quad\; -28\\ &\qquad\quad\;\overline{\;20\;}\\ &\qquad\;\; -20\\ &\qquad\quad\;\overline{\;0\;}\\ \end{matrix}$


3. Convert into decimal fraction $4\dfrac{5}{8}$

Ans: By solving given fraction

$4\dfrac{5}{8} = \dfrac{{(4 \times 8) + 5}}{8} = \dfrac{{37}}{8}$

By performing division:

$\begin{matrix} &8\overset{{4.625}}{\overline{)\;37\;}}\\ &-32\\ &\qquad\overline{\;50\;}\\ &\quad\; -48\\ &\qquad\quad\;\overline{\;20\;}\\ &\qquad\;\; -16\\ &\qquad\qquad\;\overline{\;40\;}\\ &\qquad\quad\;\; -40\\ &\qquad\qquad\;\overline{\;0\;}\\ \end{matrix}$


4. Convert into decimal fraction $\dfrac{5}{{26}}$

Ans: By performing division:

$26\overset{0.192307692}{\overline{\left){\begin{align} & \ \ 50 \\ & \underline{-26} \\ & \ \ \ 240 \\ & \ \ \underline{-234} \\ & \ \ \ \ \ 60 \\ & \ \ \ \underline{-52} \\ & \ \ \ \ \ 80 \\ & \ \ \ \underline{-78} \\ & \ \ \ \ \ \ 200 \\ & \ \ \ \ \underline{-182} \\ & \ \ \ \ \ \ 180 \\ & \ \ \ \ \underline{-156} \\ & \ \ \ \ \ \ \ 240 \\ & \ \ \ \ \ \underline{-234} \\ & \ \ \ \ \ \ \ \ \ \ 60 \\ & \ \ \ \ \ \ \ \ \underline{-52} \\ & \ \ \ \ \ \ \ \ \ \ \ \ 8 \\ \end{align}}\right.}}$


5.  Add: $37.8,56,165.08,574.6$.

Ans: By adding given numbers

$37.8+56.00+165.08+574.60=833.48$

Therefore, on adding $37.8,56,165.08,574.6$, we get $833.48 .$.


6. Subtract $27.56$ from $52.1$.

Ans: By subtracting $27.56$ from $52.1$

$52.10-27.56=24.54$

Therefore, we get $24.54$ on subtracting $25.76$ from $52.1$


7. Simplify: $42.4 - 23.57 + 53.64 - 17.8$

Ans: By adding \[42.4{\text{ and }}53.64\]

$\;\;\,42.40$

$\underline { + \,53.64}$

$\;\;96.04\;\;$    

By adding \[{\text{23}}{\text{.57 and 17}}{\text{.8}}\]  

$\;\;\,23.57$

$\underline { + \,17.80}$

$\;\;\,41.37$        

Now, by subtracting \[{\text{41}}{\text{.37 from 96}}{\text{.04}}\]

$\;\;96.04$

$\underline { - \,\,41.37}$

$\;\;54.67$


4 Mark Questions

1. Arrange the digits \[178.264\] in the place value chart. Write the place value of each digit. AIso, write \[178.264\] in expanded form.

Ans: Place value chart:

Hundred’s

Ten’s

One’s

        .

  $\dfrac{1}{{10}}{\text{th}}$

$\dfrac{1}{{100}}{\text{th}}$

$\dfrac{1}{{1000}}{\text{th}}$

          1 

        7

        8


          2

          6

          4

Expanded from:

$ 178.264 = 178 + 0.264 \\ \;\;\;\;\;\;\;\;\;\;\;\; = 1 \times 100 + 7 \times 10 + 8 \times 1 + 2 \times \dfrac{1}{{10}} + 6 \times \dfrac{1}{{100}} + 4 \times \dfrac{1}{{1000}} \\ = 100 + 70 + 8 + \dfrac{2}{{10}} + \dfrac{6}{{100}} + \dfrac{4}{{1000}} \\ $

                

2. Convert decimals into a fraction in its simplest form

(a) \[0.08\]

(b) \[0.525\]

Ans: Simplest form of given decimals can be written as

(a) $0.08 = \dfrac{8}{{100}} = \dfrac{4}{{50}} = \dfrac{2}{{25}}$

(b) $0.525 = \dfrac{{525}}{{1000}} = \dfrac{{105}}{{200}} = \dfrac{{21}}{{40}}$


3. Convert decimals as mixed fraction

(a) \[34.8\]

(b) \[4.284\]

Ans:

(a)

$34.8 = 34 + 0.8$

$ = 34 + \dfrac{8}{{10}}$

$ = 34 + \dfrac{4}{5}$

$ = 34\dfrac{4}{5}$

(b)

$4.284 = 4 + 0.284$

$ = 4 + \dfrac{{284}}{{1000}}$

$ = 4 + \dfrac{{142}}{{500}}$

$ = 4 + \dfrac{{71}}{{250}} = 4\dfrac{{71}}{{250}}$


4. Convert fractions into decimals

(a) $\dfrac{{249}}{{100}}$

(b) $\dfrac{{3104}}{{100}}$

(c) $\dfrac{{4002}}{{1000}}$

Ans:

(a) $\dfrac{{249}}{{100}} = 2.49$

(b) $\dfrac{{3104}}{{100}} = 31.04$

(c) $\dfrac{{4002}}{{1000}} = 4.002$


5 Mark Questions 

1. A student covers a journey by bus in 4 hours. He covers distance of $74 \mathrm{~km} 224 \mathrm{~m}$ during first and second hour, $58 \mathrm{~km} 56 \mathrm{~m}$ during third hour and $62 \mathrm{~km} 8 \mathrm{~m}$ during fourth hour. What is the length of his journey?

Ans: In the question, it is given that,

The distance covered during the first and second hour is $74 \mathrm{~km} 224 \mathrm{~m}$.

The distance covered during the third hour is $58 \mathrm{~km} 56 \mathrm{~m}$.

Distance covered during the fourth hour is $62 \mathrm{~km} 8 \mathrm{~m}$.

$\therefore $ Total distance covered in 4 hours is ${\text{194 km}}\;{\text{288 m}}$ .

$\;\,\,\,74\;{\text{km}}\;\,224\;{\text{m}}$

${\text{  }}\,\,\,{\text{58 km  }}\,\,{\text{56 m}}$

$\underline { + \,\,\,62\;{\text{km    }}\,\,8\;{\text{m}}\;\;}$

$\;\;\,194\,{\text{km}}\;\,\,288\,{\text{m}}$


2. Ganesh purchased a book worth $\text{Rs}\text{.}\,\text{156}\text{.65}$ from a bookseller and he gave him $\text{Rs}\text{.}\,\text{500}$ note. How much balance did he get back?

Ans: Cost of book \[ = {\text{ Rs}}{\text{. }}156.65\]

Total amount given by Ganesh \[ = {\text{ Rs}}{\text{. }}500\]

$\;\;500.00$

$\underline { - 156.65}$

$\;\;343.35$

So, the balance given by shopkeeper \[ = {\text{ Rs}}{\text{. }}343.35\]


3. The total weight of a box containing $14\;{\text{kg}}\,750\;{\text{g}}$ of mangoes, $5\;{\text{kg}}\,80\;{\text{g}}$ of apples is $22\;{\text{kg}}$ $200\;{\text{g}}$. How much is the weight of the empty box? 

Ans: Weight of mangoes $ = 14\;{\text{kg}}\,750\;{\text{g}}$

Weight of Apples $ = 5\;{\text{kg}}\,80\;{\text{g}}$

Total weight of box $ = 22\;{\text{kg}}\,200\;{\text{g}}$ 

$\;14\;{\text{kg 750g}}$

$\dfrac{{ + 5\;{\text{kg }}\;\;{\text{80g}}}}{{19\;{\text{kg}}\;830\;{\text{g}}}}$

So, the weight of empty box = total box weight - total weight of fruits

$\Rightarrow 22\,{\text{kg 200 g  -  19 kg 830 g  =  }}2\;{\text{kg}}\,370\;{\text{g}}$.


Chapter 8 - Decimals

The basic method for denoting integer and non-integer numbers is the decimal numeral system. It is the extension of the Hindu–Arabic numeral system to non-integer numbers. The decimal system's way of denoting numbers is often referred to as decimal notation.

Ex: 5.5, 24.65, 0.5, 100.18 etc.


Representing Decimals on a Number Line

A number line can be defined as a straight line with numbers positioned along its length at equal intervals or segments. In any direction, a number line can be extended indefinitely and is usually represented horizontally.

Ex: Represent the decimal number 3.75 on a number line.

Ans: 3.75 lies between 3 and 4 on a number line which is represented as follow:

(Image will be uploaded soon)


Fractions to Decimal

  • Multiply the bottom of the fraction to find a number to make it 10, or 100, or 1000, or any 1 followed by 0s.

  • By that number, multiply both top and bottom.

  • Then write down the top number only, placing the decimal point in the right position

Ex: Convert 1the fraction 4/5 into decimal notation.

Ans: 14/5 can be written as 28/10 which is obtained by multiplying 2 on both numerator and denominator. 

Now 28/10 = 2.8 is the decimal equivalent of the fraction 14/5.


Decimals to Fraction

  • Rewrite the decimal number as a fraction over one, where the numerator is the decimal number and one is the denominator.

  • Multiply both the numerator and the denominator by 10 to the power after the decimal point of the number of digits.

Ex: Convert the decimal number 2.4 into a fraction.

Ans: 2.4 can be written as 2 + 4/10. 

Further, we can write 2 as 20/10.

So 2.4 = 2 + 4/10 = 20/10 + 4/10 = 24/10 is the fractional notation of the decimal number 2.4.


Comparing Decimals

Start at the tenth position when comparing decimals. The decimal is higher for the largest value there. Shift to the hundredth position if they are the same and compare these values. Keep going to the right until you find one that is better or until you find that they are equal if the values are still the same.

Ex: Compare the decimal values and arrange them in ascending order.

2.49, 1.54, 3.65, 3.68, 4.12, 1.48, 2.44.

Ans: In the given series the least number is 1.48 and the greatest number is 4.12. 

So 1.48 < 1.54 < 2.44 < 2.49 < 3.65 < 3.68 < 4.12

Therefore ascending order of the given decimal numbers are

1.48, 1.54, 2.44, 2.49, 3.65, 3.68, 4.12.


Addition of Decimals

  • Mark the numbers up vertically such that they all sit on a vertical line with the decimal points.

  • To the right of the number, add extra zeros, so that each number has the same number of digits to the right of the decimal place.

  • Place the result's decimal point in line with the other decimal points.

Ex: Add 2.46 and 1.72.

Ans: First add the numbers in Hundredth place and next move to tenths place and finally add the numbers in one place.


Ones

Tenths

Hundredths


2

4

6

+

1

7

2

Sum

4

1

8

So, sum of 2 decimal numbers 2.46 + 1.72 = 4.18.


Subtraction of Decimals

  • Mark the numbers up vertically such that they all sit on a vertical line with the decimal points.

  • To the right of the number, add extra zeros, so that each number has the same number of digits to the right of the decimal place.

  • As you would whole numbers, deduct the numbers. Place the result's decimal point in line with the other decimal points.

Ex: Subtract 1.57 from 3.24.

Ans: Start subtracting from Hundredth place and next move to tenths place and finally ones place.


Ones

Tenths

Hundredths


3

2

4

-

1

5

7

Difference

1

6

7

So the subtraction of the two decimals is 3.24 - 1.57 = 1.67.


Benefits of Class 6 Maths Chapter 8 Decimals Important Questions

  • Proper practice is essential before any examination. With the help of important questions for Class 6 Maths Chapter 8, students will be able to practise more before their examination.

  • The experts at Vedantu have studied the previous years’ question papers in order to formulate these important questions. Thus, students can figure out the most important topics from the chapter by referring to the questions.

  • Vedantu experts have also provided solutions to important questions. These solutions have been explained using descriptions, examples, tables, and much more in order to develop an interest in students. They can strengthen their concepts with the help of important questions.

  • During exams, revision is essential for students. These important questions will help students revise the chapter. By solving the questions, they can complete the chapter easily and save some time for revision.

  • Experts at Vedantu have created these solutions according to the CBSE guidelines. Thus, students can refer to the solutions and understand the proper answering format that they have to follow in order to score good marks in the examinations. Referring to the questions and solutions will help them improve their answering skills as well.

 

Conclusion

To study more important questions and solutions on Decimals, students can download the free PDF available on Vedantu which provides top-notch solutions. These solutions provide a step by step solution to all the questions such that all the doubts of students are getting solved. Also, the extra questions in PDF provide a practice exercise for the students to improve their subject knowledge.


Important Related Links for CBSE Class 6 Maths 

FAQs on Important Questions for CBSE Class 6 Maths Chapter 8 - Decimals

1. What is a decimal?

Decimal numbers are a type of number in Maths.  A Decimal is depicted by a dot. A decimal number consists of a whole number and a fractional part. Decimal forms an important concept in math. Decimal numbers can be placed on a number line. Decimals are used in weights, as a measure of distance and even the products that we buy have a maximum retail price that contains a decimal. Examples of decimal numbers are 0.5, 1.85, and 27.578.

2. Can we depict a decimal number on a number line?

Yes. Decimal numbers can be depicted on a number line. Each decimal number will have a unique place on the number line just like the whole numbers. When you draw a number line, you mark certain points as representing the whole numbers. The space between them represents various small and infinite numbers that come between them. A decimal number will come between two whole numbers when drawn on a number line. For example, if you want to draw a number, say 3.5, the number will be placed in the middle of the number 3 and number 4.

3. Is Chapter 8 of Class 6 Maths important?

Decimals help us to express various quantities or measures. We use decimals in our daily life knowingly or unknowingly. The chapter on decimals will help you understand the need and basis of decimals. In your higher classes, it will be expected of you that you have a basic knowledge and understanding of decimals. Decimals will form an important part of not only your math curriculum. They will also be crucial in your science and economics. The chapter is important because it helps you develop your foundation for the whole world of decimals, numbers and measures that you will be exploring later in your school life.

4. How do you show 0.2 on a number line?

The number line allows us to depict various numbers. The ruler you use will give you an idea about how a number line works and helps us in our daily life. Various numbers are marked on the number line. The space between them tells us that several smaller numbers exist between two numbers. If you want to draw 0.5 on a number line, you will know that the number is greater than 0 but smaller than 1. The 5 after the decimal tells you how much it is away from the 0 or how much it is closer to 1. It is 5 away from 0 and 1. This means that it will be placed in the middle of 0 and 1.

5. How should I approach Chapter 8 of Class 6 Maths?

Chapter 8 of Class 6 describes decimals to you. To understand the concept, make sure that you are regular to your classes. Go through the text once in your free time after it has been taught by the teacher. The language of the book is such that you understand the concepts easily. Make short notes. Practice the examples and the questions given in the textbook. Revise the notes daily. Seek your teacher’s help when you have a doubt.