Ncert Solutions For Class 6 Maths Ex 8.1

Ncert Solutions For Class 6 Maths Chapter 8 Ex 8.1

1. Using the given diagram write the data in form of numbers in the table given below:

1

Hundreds (100) Tens

(10)

Ones

(1)

Tenths

(\(\frac{1}{10}\))

Answer:

 

Hundreds (100) Tens

(10)

Ones

(1)

Tenths

(\(\frac{1}{10}\))

Number
0 3 1 2 31.2
1 1 0 4 110.4

 

2. Write the given decimals in the place value table.

(a) 20.4

(b) 0.4

(c) 18.5

(d) 302.1

 

Answer:

Hundreds (100) Tens

(10)

Ones

(1)

Tenths

(\(\frac{1}{10}\))

Number
(a) 0 2 0 4 20.4
(b) 0 0 0 4 0.4
(c) 0 1 8 5 18.5
(d) 3 0 2 1 302.1

 

 

3. Write the given values in the form of decimals:

(a) five-tenths

(b) Four tens and seven-tenths

(c) Sixteen point three

(d) Six hundred and eight-ones

(e) Nine hundred point one

 

Answer:

(a) five-tenths = 5 tenths

= \(\frac{5}{10}\)

= 0.5

 

(b) Four tens and seven-tenths = 4 tens and 7 tenths

= \((4 \times 10) + \frac{7}{10}\)

= 40 + 0.7

= 40.7

 

(c) Sixteen point three = 16.3

 

(d) Six hundred and eight-ones = 6 hundreds + 8 ones

= 600 + 8

= 608

 

(e) Nine hundred point one = 900.1

 

4. Write the fractions given below in the form of 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) \(4\frac{1}{2}\)

 

Answer:

(a) \(\frac{5}{10}\) = 0.5

 

(b) \(3 + \frac{7}{10}\) = 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 + 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) \(\frac{2}{5}\) = \(\frac{2 \times 2}{5 \times 2}\)

= \(\frac{4}{10}\)

= 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

 

5. Write the given decimals in the form of fraction. Reduce them to the lowest terms:

(a) 0.6

(b) 2.5

(c) 1.0

(d) 3.8

(e) 13.7

(f) 21.2

(g) 6.4

 

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 = \(\frac{64}{10}\)

= \(\frac{32}{5}\)

 

6. Express the following as cm using decimals:

(a) 30 mm

(b) 2 mm

(c) 116 mm

(d) 4cm 2mm

(e) 162 mm

(f) 83 mm

Answer:

(a) Since, 10mm = 1cm

Therefore, 1mm = \(\frac{1}{10}\) cm

Therefore, 30mm = \(\frac{1}{10}\) x 30 = 3.0cm

 

(b) Since, 10 mm =1cm

Therefore, 1mm = \(\frac{1}{10}\) cm

Therefore, 2mm = \(\frac{1}{10}\) x 2 = 0.2 cm

 

(c) Therefore, 116 mm = \(\frac{1}{10}\) x 116 = 11.6 cm

 

(d) Since, 10mm = 1cm

\(4cm+\frac{2}{10}cm\)

4 + 0.2 = 4.2 cm

 

(e) 1mm = \(\frac{1}{10}\) cm

162 mm = \(\frac{1}{10}\times 162 =16.2cm\)

 

(f) Since, 10 mm = 1cm

Therefore, 1mm = \(\frac{1}{10}\) cm

Therefore, 83 mm = \(\frac{1}{10}\times 83 =8.3cm\)

 

7. Between which two whole numbers do the given numbers lie? Then find the closest whole number to the given numbers.

2

(a) 5.1

(b) 0.8

(c) 6.4

(d) 2.6

(e) 4.9

(f) 9.1

Answer:

(a) From 5 to 6, 5.1 is nearest to 5.

(b) From 0 to 1, 0.8 is nearest to 1.

(c) From 6 to 7, 6.4 is nearest to 6.

(d) From 2 to 3, 2.6 is nearest to 3.

(e) From 4 to 5, 4.9 is nearest to 5.

(f) From 9 to 10, 9.1 is nearest to 9

 

8. Show the given numbers on number line:

(a) 0.2

(b)1.9

(c) 1.1

(d) 2.5

Answer:

3

 

9. From the given number line, write down decimal number represented by the points P, Q, R and S.

4

Answer:

P = 0 + \(\frac{8}{10}\)

= 0.8

 

Q = 1 + \(\frac{3}{10}\)

= 1 + 0.3

= 1.3

 

R = 2 + \(\frac{2}{10}\)

= 2 + 0.2

= 2.2

 

S = 2 + \(\frac{9}{10}\)

= 2 + 0.9

= 2.9

 

10. (a) The length of Mahesh’s textbook is 10 cm and 6 mm. What will be the length of textbook in cm?

(b) The length of a rose plant is 75 mm. Write the length in cm form.

 

Answer:

(a) 10 cm 6 mm = 9 cm + 6 mm

= 9 + \(\frac{6}{10}\)

= 9.6 cm

 

(b) 75 mm = \(\frac{75}{10}\) cm

= 7.5 cm

 

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