NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1

These NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 8 Decimals Ex 8.1

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

Answer:

Question 2.
Write the following decimals in the place value table.
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9
Answer:

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
Answer:
(a) The decimal-form of seven-tenths is 7 = \(\frac{7}{10}\) = 0.7
(b) 2 tens and 9-tenths
= 2 x 10 + \(\frac{9}{10}\) = 20 + 0.9
= 20.9
(c) Fourteen point six = 14.6
(d) One hundred and 2-ones
= 100 + 2 x 1 = 100 + 2 = 102
(e) Six hundred point eight = 600.8

Question 4.
Write each of the following as decimals:
Answer:
(a) \(\frac{5}{10}\) = 0.5
(b) 3 + \(\frac{7}{10}\) = 3 + 0.7 = 3.7
(c) 200 + 60 + 5 + \(\frac{1}{10}\)
= 200 + 60 + 5 + 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 + 0.8 = 8.8
(f) 4\(\frac{2}{10}\) = 4 + \(\frac{2}{10}\) = 4 + 0.2 = 4.2
(g) \(\frac{3}{2}=\frac{3 \times 5}{2 \times 5}=\frac{15}{10}=\frac{10+5}{10}\)
= \(\frac{10}{10}+\frac{5}{10}\) = 1 + 0.5 = 1.5
(h) \(\frac{2}{5}=\frac{2 \times 5}{5 \times 2}=\frac{4}{10}\) = 0.4
(i) \(\frac{12}{5}=\frac{12 \times 2}{5 \times 2}=\frac{24}{10}=\frac{20+4}{10}\)
= \(\frac{20}{10}+\frac{4}{10}\) = 2 + 0.4 = 2.4
(j) \(3 \frac{3}{5}=3+\frac{3}{5}=3+\frac{3 \times 2}{5 \times 2}\)
= 3 + \(\frac{6}{10}\) = 3 + 0.6 = 3.6
(k) \(4 \frac{1}{2}=4+\frac{1}{2}=4+\frac{1 \times 5}{2 \times 5}\)
= 4 + \(\frac{5}{10}\) = 4 + 0.5 = 4.5

Question 5.
Write the following decimals as fractions. Reduce the fractions to lowest form.
Answer:
(a) 0.6 = \(\frac{6}{10}=\frac{3}{5}\)
(b) 2.5 = \(\frac{25}{10}=\frac{5}{2}\)
(c) 1.0 = \(\frac{10}{10}\) = 1
(d) 3.8 = \(\frac{38}{10}=\frac{19}{5}\)
(e) 13.7 = \(\frac{137}{10}\)
(f) 21.2 = \(\frac{212}{10}=\frac{106}{5}\)
(g) 6.4 = \(\frac{64}{10}=\frac{32}{5}\)

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
Answer:
(a) ∵ 10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 2 mm = \(\frac { 1 }{ 10 }\) x 2 = 0.2 cm

(b) ∵10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm
∴ 30 mm = \(\frac { 1 }{ 10 }\) x 20 = 3.0 cm

(c) ∵ 10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm 10
∴ 116 mm = \(\frac { 1 }{ 10 }\) x 116 = 11.6 cm

(d) ∵ 10 mm = 1 cm
4 cm 2 mm = 4 + \(\frac { 2 }{ 10 }\) cm 10
= 4 + 0.2 = 4.2 cm

(e) ∵ 10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm 10
∴ 162 mm = \(\frac { 1 }{ 10 }\) x 162 = 16.2 cm 10

(f) ∵ 10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm 10
∴ 83 mm =\(\frac { 1 }{ 10 }\) x 83 = 8.3 cm 10

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?

(a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9
Answer:
(a) 0.8 lies between 0 and 1, 0.8 is nearer to 1
(b) 5.1 lies between to 6,5.1 is nearer to 5.
(c) From 2 to 3, 2.6 is nearest to 3.
(d) 2.6 lies between 6 to 7, 6.4 is nearer to 6.
(e) 9.1 lies between 9 to 10,9.1 is nearer to 9.
(f) 4.9 lies between 4 to 5, 4.9 is nearer to 5.

Question 8.
Show the following numbers on the number line:
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5
Answer:

Question 9.
Write the decimal number represented by the points A, B, C, D on the given number line.

Answer:
A = 0 + \(\frac{8}{10}\) = 0.8
B = 1 + \(\frac{3}{10}\) = 1.3
C = 2 + \(\frac{2}{10}\) = 2.2
D = 2 + \(\frac{9}{10}\) = 2.9

Question 10.
(a) The length of Ramesh’s notebook is 9 cm and 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.
Answer:
(a) 9 cm 5 mm = 9 cm + 5 mm
= 9 + \(\frac{5}{10}\) = 9.5 cm
(b) 65 mm = \(\frac{65}{10}\) cm = 6.5 cm