Important Questions for CBSE Class 6 Maths 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:

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.

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.

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.

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