GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

   

Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 1.
Write the following as numbers in the given table.
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 1
Solution:
(a) In the given figure there are:
3 towers (each of 10 units), one block (equal to 1 unit), and 2 small parts (each equal to 2 tenths). So, we can write in the given table as:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 2
(b) In the figure, there are:
1 hundred, 1 ten, 0 units, and 4 tenths. So given table is written as:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 3

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 2.
Write the following decimals in the place value table.
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9
Solution:
(a) 19.4
∵ 19.4 = 1 × 10 + 9 × 1 + 4 × \(\frac { 1 }{ 10 }\)
∴ We have,
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 4
(b) 0.3
∵ 0.3 = 0 + \(\frac { 3 }{ 10 }\)
∴ We have,
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 5
(c) 10.6
∵ 10.6 = 1 × 10 + 0 × 1 + 6 × \(\frac { 1 }{ 10 }\)
∴ We have,
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 6
(d) 205.9
∵ 205.9 = 2 × 100+ 0 × 10 +5 × 1 +9 × \(\frac { 1 }{ 10 }\)
∴ We have,
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 7

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 3.
Write each of the following as decimals:
(a) Seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two ones
(e) Six hundred point eight
Solution:
(a) Seven-tenths:
We have seven-tenths = 7 × \(\frac { 1 }{ 10 }\) = 0.7

(b) Two tens and nine-tenths:
We have, two tens and nine-tenths
= 2 × 10 + 9 × \(\frac { 1 }{ 10 }\) = 20 + \(\frac { 9 }{ 10 }\)
= 20 + 0.9 = 20.9

(c) Fourteen point six:
We have, fourteen point six = 14.6

(d) One hundred and two ones:
We have, one hundred and two = 1 hundred + 0 tens + 2 ones + 0 tenths
= 100 + 0 + 2 + \(\frac { 0 }{ 10 }\) = 102.0

(e) Six hundred point eight:
We have, 6 hundred points 8 = 600.8

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 4.
Write each of the following as decimals:
(a) \(\frac { 5 }{ 10 }\)
(b) 3 + \(\frac { 7 }{ 10 }\)
(c) 200 + 60 + 5 + \(\frac { 1 }{ 10 }\)
(d) 70 + \(\frac { 8 }{ 10 }\)
(e) \(\frac { 88 }{ 10 }\)
(f) 4\(\frac { 2 }{ 10 }\)
(g) \(\frac { 3 }{ 2 }\)
(h) \(\frac { 2 }{ 5 }\)
(i) \(\frac { 12 }{ 5 }\)
(j) 3\(\frac { 3 }{ 5 }\)
(k) 4\(\frac { 1 }{ 2 }\)
Solution:
(a) \(\frac { 5 }{ 10 }\) = 0.5

(b) 3 + \(\frac { 7 }{ 10 }\) = 3 + 0.7 = 3.7

(c) 200 + 60 + 5 + \(\frac { 1 }{ 10 }\) = 265 + 0.1 = 265.1

(d) 70 + \(\frac { 8 }{ 10 }\) = 70 + 0.8 = 70.8

(e) \(\frac { 88 }{ 10 }\) = \(\frac{80+8}{10}\) = \(\frac { 80 }{ 10 }\) + \(\frac { 8 }{ 10 }\) = 8 + \(\frac { 8 }{ 10 }\) = 8.

(f) 4\(\frac { 2 }{ 10 }\) = 4 + 4\(\frac { 2 }{ 10 }\) = 4.2

(g) \(\frac { 3 }{ 2 }\)
Since, \(\frac { 3 }{ 2 }\) = \(\frac { 3 × 5 }{ 2 × 5 }\) = \(\frac { 15 }{ 10 }\) = \(\frac { 10 + 5 }{ 10}\)
= \(\frac { 10 }{ 10 }\) + \(\frac { 5 }{ 10 }\) = 1 + \(\frac { 5 }{ 10}\) = 1.5
Thus,\(\frac { 3 }{ 2 }\) = 1.5

(h) \(\frac { 2 }{ 5 }\)
Since, \(\frac { 2 }{ 5 }\) = \(\frac { 2 × 2 }{ 5 × 2 }\) = \(\frac { 4 }{ 10 }\) = 0.4
∴ \(\frac { 2 }{ 5 }\) = 0.4

(i) \(\frac { 12 }{ 5 }\)
Since, \(\frac { 12 }{ 5 }\) × \(\frac { 2 }{ 2 }\) = \(\frac { 24 }{ 10 }\) = \(\frac { 20 + 4 }{ 10 }\) = \(\frac { 20 }{ 10 }\) + \(\frac { 4 }{ 10 }\)
= 2 + \(\frac { 4 }{ 10 }\) = 2.4

(j) 3\(\frac { 3 }{ 5 }\)
Since, 3\(\frac { 3 }{ 5 }\) = 3 + \(\frac { 3 }{ 5 }\) = 3 + \(\left(\frac{3}{5} \times \frac{2}{2}\right)\)
= 3 + \(\frac { 6 }{ 10 }\) = 3.6

(k) 4\(\frac { 1 }{ 2 }\)
Since, 4\(\frac { 1 }{ 2 }\) = 4 + \(\frac { 1 }{ 2 }\) = 4 + 4\(\frac { 1 × 5 }{ 2 × 5 }\)
= 4 + 4\(\frac { 5 }{ 10 }\) = 4.5

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 5.
Write the following decimals as fractions. Reduce the fractions to the lowest form.
(a) 0.6
(b) 2.5
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6-4
Note: To convert a decimal to a fraction, we have the following steps:
I. Count the number of digits in the decimal part.
II. Ignoring the decimal point, write all the given digits as the numerator of the fraction.
III. In the denominator write as many zeros after 1 as there are decimal places in the decimal fraction.
IV. Reduce the fraction, so obtained, to its simplest form.
Solution:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 8

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 6.
Express the following as cm using decimals,
(a) 2 mm
(b) 30 mm
(c) 116 mm
(d) 4 cm 2 mm
(e) 162 mm
(f) 83 mm
Solution:
(a) 2 mm:
∵ 10 mm = 1 cm or 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 2 mm = \(\frac { 1 }{ 10 }\) × 2 mm = \(\frac { 2 }{ 10 }\) cm = 0.2 cm

(b) 30 mm
∵ 10 mm = 1 cm or 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 30 mm = \(\frac { 1 }{ 10 }\) × 30 mm = \(\frac { 30 }{ 10 }\) cm = 3.0 cm

(c) 116 mm
∵ 10 mm = 1 cm or 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 116 mm = \(\frac { 1 }{ 10 }\) × 116 mm = \(\frac { 116 }{ 10 }\) cm
= \(\frac { 116 + 6 }{ 10 }\) cm = \(\left(\frac{110}{10}+\frac{6}{10}\right)\) cm
= \(\left(11+\frac{6}{10}\right)\) cm = 11.6 cm

(d) 4 cm 2 mm
We have : 4 cm 2 mm = 4 cm + 2 mm
= 4 cm + \(\frac { 2 }{ 10 }\) cm
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 9
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 10

(e) 162 mm:
∵ 10 mm = 1 cm or 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 162 mm = \(\frac { 1 }{ 10 }\) × 162 cm = \(\frac { 162 }{ 10 }\) cm
= \(\frac { 162 + 2 }{ 10 }\) cm = GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 11
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 12

(f) 83 mm:
∵ 10 mm = 1 cm or 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 83 mm = \(\frac { 1 }{ 10 }\) × 83 cm = \(\frac { 83 }{ 10 }\) cm
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 13

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 7.
Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number?
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 14
(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9
Solution:
(a) 0.8:
0.8 lies between 0 and 1 and 1 are nearer to 0.8.

(b) 5.1:
5.1 lies between 5 and 6 and 5 are nearer to 5.1.

(c) 2.6:
2.6 lies between 2 and 3 and 3 are nearer to 2.6.

(d) 6.4:
6.4 lies between 6 and 7 and 6 are nearer to 6.4.

(e) 9.1:
9.1 lies between 9 and 10 and 9 are nearer to 9.1.

(f) 4.9:
4.9 lies between 4 and 5 and 5 are nearer to 4.9.

Question 8.
Show the following numbers on the number line.
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5
Solution:
(a) 0.2
0.2 lies between 0 and 1
∴ Divide the unit length between 0 and 1 into 10 equal parts and take 2 parts as shown below. A
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 15
(b) 1.9
1.9 lies between 1 and 2
∴ Divide the unit length between 1 and 2 into 10 equal parts and take 9 parts as shown below:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 16
Point B represents 1.9.
(c) 1.1
1.1 lies between 1 and 2. Divide the unit length between 1 and 2 into 10 equal parts and take 1 part as shown below:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 17
Thus, point C represents 1.1.
(d) 2.5
2.5 lies between 2 and 3. Divide the unit length between 2 and 3 into 10 equal parts and take 5 parts as shown below:
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 18

Thus, point D represents 2.5.

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 9.
Write the decimal number represented by the points A, B, C, D on the given number line.
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 19
Solution:
(i) Point A: Point A lies between 0 and 1. The unit distance between 0 and 1 is divided into 10 equal parts. Point A stands at the 8th part.
Thus, 0.8 is represented by A

(ii) Point B: Point B lies between 1 and 2. The unit distance between 1 and 2 is divided into 10 equal parts and point B is at the 3rd part.
Thus, 1.3 is represented by B.

(iii) Point C: The point C lies between 2 and 3. The unit distance between 2 and 3 is divided into 10 equal parts and C is at the 2nd part. Thus, 2.2 is represented by C.

(iv) Point D: The point D lies between 2 and 3. The distance between 2 and 3 is divided into 10 equal parts and the 9 parts have been taken.
∴ 2.9 is represented by D.

GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1

Question 10.
(a) The length of Ramesh’s notebook is 9 cm 5 mm. What will be its length in cm?
(b) The length of a young gram plant is 65 mm. Express its length in cm.
Solution:
(a) Length of Ramesh’s notebook = 9 cm 5 mm
But 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 5 mm = 5 × \(\frac { 1 }{ 10 }\) cm = \(\frac { 5 }{ 10 }\) cm = 0.5 cm
Now 9 cm 5 mm = 9.5 cm
Thus, the length of the notebook = 9.5 cm

(b) ∵ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 65 mm = 65 × \(\frac { 1 }{ 10 }\) cm
= \(\frac { 65 }{ 10 }\) cm = \(\frac { 65 + 5 }{ 10 }\) cm
GSEB Solutions Class 6 Maths Chapter 8 Decimals Ex 8.1 img 20

Leave a Comment

Your email address will not be published. Required fields are marked *