NCERT Solutions for Class 6 Maths Chapter 8: Decimals - Exercise 8.1

Exercise 8.1

1. Write the following as numbers in the given table: 

(a) 

Ans: Count the number of cells in each category to get the value for tables.

I. Since there are no cells of Hundreds. So, the value for the column of hundreds in the table is 0.

II. Since there are 3 cells of Tens. So, the value of the column of tenth in the table is 3.

III. Since there is 1 cell of Ones. So, the value of the column of ones in the table is 1.

IV. Since there are 2 cells of Tenths. So, the value of the column of tenths in a table is 2.

(b) 

Ans: Count the number of cells in each category to get the value for tables.

I. Since there is 1 cell of Hundreds. So, the value for a column of hundreds in the table is 1.

II. Since there is 1 cell of Tens. So, the value of the column of tenth in the table is 1.

III. Since there is 0 cell of Ones. So, the value of the column of ones in a table is 0.

IV. Since there are 4 cells of Tenths. So, the value of the column of tenths in table is 4.

2. Write the following decimals in the place value table:

(a) $19.4$

Ans: Observe the digits at places to find the table of place values.

I. Since there is 1 as digits in the Tens place. So, the value for a column of Tens in the table is 1.

II. Since there is 9 as digits in One place. So, the value of the column of Ones in the table is 9.

III. Since there are 4 digits in Tenths place. So, the value of the column of tenths in the table is 4.

(b )$0.3$

Ans: Observe the digits at places to find the table of place values.

I. Since there is 0 as a digit in One’s place. So, the value of the column of Ones in the table is 0.

II. Since there are 3 as digits in Tenths place. So, the value of the column of tenths in the table is 3.

(c) $10.6$

Ans: Observe the digits at places to find the table of place values.

I. Since there is 1 as a digit in Tens place. So, the value for a column of Tens in the table is 1.

II. Since there is 0 as a digit in One’s place. So, the value of the column of Ones in the table is 0.

III. Since there are 6 as digits in Tenths place. So, the value of the column of tenths in the table is 6.

(d) $205.9$

Ans: Observe the digits at places to find the table of place values.

I. Since there are 2 digits cells of Hundreds. So, the value for a column of hundreds in the table is 2.

II. Since there is 0 as digits cells of Tens. So, the value of the column of tenth in the table is 0.

III. Since there are 5 as digits cells of Ones. So, the value of the column of ones in the table is 5.

IV. Since there are 9 as digits cells of Tenths. So, the value of the column of tenths in the table is 9.

3. Write each of the following as decimals:

(a) seven-tenths

Ans: Since seven is given in tenths position.

So, it can be written as $\dfrac{7}{{10}} = 0.7$

(b) Two tens and nine-tenths

Ans: Since two is given in tens position and nine is given in tenths position.

So, it can be written as $2 \times 10 + \dfrac{9}{{10}} = 20.9$

(c) Fourteen point six

Ans: Since Fourteen is given before decimals and six is given after decimals.

So, it can be written as $14.6$.

(d) One hundred and 2-ones

Ans: Since one is given in a hundred places and 2 is given at one’s place.

So, it can be written as $1 \times 100 + 2 \times 1 = 102$.

(e) Six hundred point eight

Ans: Since six is given in hundred places and is given before decimals and eight is given after decimals.

So, it can be written as $6 \times 100 + 0.8 = 600.8$.

4. Write each of the following as decimals:

(a) $\dfrac{5}{{10}}$

Ans: Divide 5 with 10 to get in the decimal form.

So, it can be written as  $\dfrac{5}{{10}} = 0.5$

(b) $3 + \dfrac{7}{{10}}$

Ans: Divide 7 with 10 to get in decimal form and add 3 to the obtained value.

So, it can be written as  $3 + \dfrac{7}{{10}} = 3 + 0.7 = 3.7$

(c) \[200 + 60 + 5 + \dfrac{1}{{10}}\]

Ans: Divide 1 with 10 to get in decimal form and add 200, 60, 5 to the obtained value.

So, it can be written as \[200 + 60 + 5 + \dfrac{1}{{10}} = 200 + 60 + 5 + 0.1 = 265.1\]

(d) \[70 + \dfrac{8}{{10}}\]

Ans: Divide 8 with 10 to get in decimal form and add 70 to the obtained value.

So, it can be written as \[70 + \dfrac{8}{{10}} = 70 + 0.8 = 70.8\].

(e) \[\dfrac{{88}}{{10}}\]

Ans: Divide 88 with 10 to get in decimal form.

So, it can be written as \[\dfrac{{88}}{{10}} = 8.8\].

(f) \[4\dfrac{2}{{10}}\]

Ans: Convert mixed fraction into a proper fraction by multiplying 4 with the denominator and adding 2 to it. Divide 42 with 10 to get in decimal form.

So, it can be written as \[4\dfrac{2}{{10}} = \dfrac{{42}}{{10}} = 4.2\]

(g) \[\dfrac{3}{2}\]

Ans: Multiply 5 to numerator and denominator to get 10 as the denominator.

Divide 15 with 10 to get in decimal form.

So, it can be written as \[\dfrac{3}{2} = \dfrac{{3 \times 5}}{{2 \times 5}} = \dfrac{{15}}{{10}} = 1.5\].

(h) \[\dfrac{2}{5}\]

Ans: Multiply 2 to numerator and denominator to get 10 as the denominator.

Divide 4 with 10 to get in decimal form.

So, it can be written as \[\dfrac{2}{5} = \dfrac{{2 \times 2}}{{5 \times 2}} = \dfrac{4}{{10}} = 0.4\].

(i) \[\dfrac{{12}}{5}\]

Ans: Multiply 2 to numerator and denominator to get 10 as the denominator.

Divide 24 with 10 to get in decimal form.

So, it can be written as \[\dfrac{{12}}{5} = \dfrac{{12 \times 2}}{{5 \times 2}} = \dfrac{{24}}{{10}} = 2.4\].

(j) \[3\dfrac{3}{5}\]

Ans: Convert mixed fraction into a proper fraction by multiplying 3 with denominator and adding 3 to it. Multiply 2 to numerator and denominator to get 10 as the denominator.

Divide 36 with 10 to get in decimal form.

So, it can be written as \[3\dfrac{3}{5} = \dfrac{{18 \times 2}}{{5 \times 2}} = \dfrac{{36}}{{10}} = 3.6\].

(k) \[4\dfrac{1}{2}\]

Ans: Convert mixed fraction into a proper fraction by multiplying 4 with the denominator and adding 1 to it. Multiply 5 to numerator and denominator to get 10 as the denominator.

Divide 45 with 10 to get in decimal form.

So, it can be written as \[4\dfrac{1}{2} = \dfrac{{9 \times 5}}{{2 \times 5}} = \dfrac{{45}}{{10}} = 4.5\].

5. Write the following decimals as fraction. Reduce the fractions to lowest terms.

(a) $0.6$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $0.6 = \dfrac{6}{{10}} = \dfrac{3}{5}$.

(b) $2.5$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $2.5 = \dfrac{{25}}{{10}} = \dfrac{5}{2}$.

(c) $1.0$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $1.0 = \dfrac{{10}}{{10}} = 1$.

(d) $3.8$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $3.8 = \dfrac{{38}}{{10}} = \dfrac{{19}}{5}$.

(e) $13.7$

Ans: Convert decimal into fractions. 

So, it can be written as $13.7 = \dfrac{{137}}{{10}}$.

(f) $21.2$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $21.2 = \dfrac{{212}}{{10}} = \dfrac{{106}}{5}$.

(g) $6.4$

Ans: Convert decimal into fractions. Eliminate common factors to convert the fraction to the simplest form.

So, it can be written as $6.4 = \dfrac{{64}}{{10}} = \dfrac{{32}}{5}$.

6. Express the following as cm using decimals:

(a) ${\text{2 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form.

So, it can be written as ${\text{2 mm = }}\dfrac{2}{{{\text{10}}}}{\text{ cm = 0}}{\text{.2 cm}}$.

(b) ${\text{30 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form.

So, it can be written as ${\text{30 mm = }}\dfrac{{30}}{{{\text{10}}}}{\text{ cm = 3}}{\text{.0 cm}}$.

(c) ${\text{116 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form.

So, it can be written as \[{\text{116 mm = }}\dfrac{{116}}{{{\text{10}}}}{\text{ cm = 11}}{\text{.6 cm}}\].

(d) ${\text{4 cm 2 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form. Add 4 to it to get the required value.

So, it can be written as \[{\text{4 cm 2 mm = 4 + }}\dfrac{2}{{{\text{10}}}}{\text{ cm = 4}}{\text{.2 cm}}\].

(e) ${\text{162 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form. 

So, it can be written as \[{\text{162 mm = }}\dfrac{{162}}{{{\text{10}}}}{\text{ cm = 16}}{\text{.2 cm}}\].

(f) ${\text{83 mm}}$

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form. 

So, it can be written as \[{\text{83 mm = }}\dfrac{{83}}{{{\text{10}}}}{\text{ cm = 8}}{\text{.3 cm}}\].

7. Between which two whole numbers on the number line are the given lie? Which of these whole numbers is nearer the number?

(a) $0.8$

Ans: $0.8$ lies between 0 and 1 and It is closer to 1.

(b) $5.1$

Ans: $5.1$ lies between 5 and 6 and It is closer to 5.

(c) $2.6$

Ans: $2.6$ lies between 2 and 3 and It is close to 3.

(d) $6.4$

Ans: $6.4$ lies between 6 and 7 and It is closer to 6.

(e) $9.1$

Ans: $9.1$ lies between 9 and 10 and It is closer to 9.

(f) $4.9$

Ans: $4.9$ lies between 4 and 5 and It is closer to 5.

8. Show the following numbers on the number line: 

(a) $0.2$

Ans: Plot the given number on a number line.

(b) $1.9$

Ans: Plot the given number on a number line.

(c) $1.1$

Ans: Plot the given number on a number line.

(d) $2.5$

Ans: Plot the given number on a number line.

9. Write the decimal number represented by the points A, B, C, D:

Ans: Count the points on a number line to get the value of the given points.

10. (a) The length of Ramesh’s notebook is 9 cm and 5 mm. What will be its length in cm?

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form. Add 9 to it to get the required value.

So, it can be written as \[{\text{9 cm 5 mm = 9 + }}\dfrac{5}{{{\text{10}}}}{\text{ cm = 9}}{\text{.5 cm}}\].

(b) The length of a young gram plant is 65 mm. Express its length in cm.

Ans: Divide the given value by 10 to convert mm into cm. Convert it to decimal form. 

So, it can be written as \[{\text{65 mm = }}\dfrac{{65}}{{{\text{10}}}}{\text{ cm = 6}}{\text{.5 cm}}\].

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Exercise 8.1

Opting for the NCERT solutions for Ex 8.1 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 8.1 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 8 Exercise 8.1 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 6 Maths Chapter 8 Exercise 8.1, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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