NCERT Solutions for Class 6 Maths Chapter 8 Decimals InText Questions

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

NCERT Solutions for Class 6 Maths Chapter 8 Decimals InText Questions

NCERT In-text Question Page No. 165

Question 1.
Can you now write the following as decimals?

Answer:
We have,
(i) 5 hundreds + 3 tens + 8 ones + 1 tenth
= 5 x 100 + 3 x 10 + 8 x 1 + 1 x \(\frac { 1 }{ 10 }\)
= 500 x 30 + 8 + \(\frac { 1 }{ 10 }\)
= 538 x \(\frac { 1 }{ 10 }\) = 538.1

(ii) 2 hundreds + 7 tens + 3 ones + 4 tenths
= 2 x 100 + 7 x 10 + 3 x 1 + 4 x \(\frac { 1 }{ 10 }\)
= 200 x 70 + 3 + \(\frac { 4 }{ 10 }\)
= 273 x \(\frac { 4 }{ 10 }\) = 273.4

(iii) 3 hundreds + 3 tens + 4 ones + 1 tenth
= 3 x 100 + 5 x 10 + 4 x 1 + 6 x \(\frac { 1 }{ 10 }\)
= 300 x 50 + 4 + \(\frac { 6 }{ 10 }\)
= 354 x \(\frac { 6 }{ 10 }\) = 354.6

Question 2.
Write the lengths of Ravi’s and Raju’s pencils in ‘cm’ using decimals.
Answer:
10 mm = 1 cm
Therefore, 1 mm = \(\frac { 1 }{ 10 }\) cm
So, 5 mm = 5 x \(\frac { 1 }{ 10 }\) cm = \(\frac { 5 }{ 10 }\) cm
and 3 mm = 3 x \(\frac { 1 }{ 10 }\) cm = \(\frac { 3 }{ 10 }\) cm
Now, 7 cm 5 mm = 7 cm + 5 mm
= 7 cm + \(\frac { 5 }{ 10 }\) cm
= 7.5 cm
Again
8 cm 3 mm = 8 cm + 3 mm
= 8 cm + \(\frac { 3 }{ 10 }\)cm
= 8.3 cm

Question 3.
Make three more examples similar to the one given in question 1 and solve them.
Answer:
Please try yourself.

NCERT In-text Question Page No. 167

Question 1.
Write \(\frac{3}{2}, \frac{4}{5}, \frac{8}{5}\) in decimal notation.
Answer:
(i) \(\frac{3}{2}\)
We have, \(\frac{3}{2}=\frac{3 \times 5}{2 \times 5}=\frac{15}{10}=\frac{15}{10}\) = 1.5
∴ \(\frac{3}{2}\) = 1.5

(ii) \(\frac{4}{5}\)
We have, \(\frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}\) = 0.8
= \(\frac{8}{10}\) = 0.8
Thus, \(\frac{4}{5}\) = 0.8

(iii) \(\frac{8}{5}\)
We have, \(\frac{8}{5}=\frac{8 \times 5}{5 \times 5}=\frac{16}{10}\) = 1.6
Thus, \(\frac{8}{5}\) = 1.6

NCERT In-text Question Page No. 175

Question 1.
(i) Write 2 rupees 5 paise and 2 rupees 50 paise in decimals.
(ii) Write 20 rupees 7 paise and 21 rupees 75 paise in decimals.
Answer:
(i) (a) 2 rupees 5 paise :
2 rupees + 5 paise = 2 rupees + \(\frac{5}{10}\) rupees
∵ 100 paise = ₹1
∴ 1 paise = ₹ \(\frac{1}{100}\)
= (2 + 0.05) rupees = ₹2.05

(b) 2 rupees 50 paise =
2 rupees + 50 paise = 2 rupee + \(\frac{50}{100}\) rupees
∵ 100 paise = ₹1
∴ 1 paise = ₹ \(\frac{1}{100}\)
= (2 + 0.50) rupees = ₹ 2.50

(ii) (a) 20 rupees 7 paise :
20 rupees +7 paise
= 20 rupees + 7 x\(\frac{1}{100}\) rupees
[ ∴ \(\frac{1}{100}\) rupee = 1 paise]
= 20 rupees + 0.07 rupee
= ₹ (20 + 0.07)
= ₹ 20.07

(b) 21 rupees 75 paise :
21 rupees + 75 paise
= 21 rupees + 75 x -jy rupees
= 21 rupees + -jy rupees
= ₹ [21 + 0.75] = ₹ 21.75

NCERT In-text Question Page No. 176

Question 1.
Can you write 4 mm in ’em’ using decimals?
Answer:
Yes,
Since 10 mm = 1 cm
∴ 1 mm = \(\frac { 1 }{ 10 }\) cm
or 4 mm = 4 x \(\frac { 1 }{ 10 }\) cm = 0.4 cm

Question 2.
How will you write 7 cm 5 mm in ’em’ using decimals.
Answer:
7 cm 5 mm:
Since, 10 mm = 1 cm
∴ 1 mm= \(\frac { 1 }{ 10 }\) cm
Now, 7 cm 5 mm = 7 cm + 5 mm
= 7 cm + 5 x \(\frac { 1 }{ 10 }\) cm =[ 7 + \(\frac { 5 }{ 10 }\) cm
= (7 + 0.5) cm = 7.5 cm

Question 3.
How will you write 2008 m in ‘km’?
Answer:
Yes, we can change the given ‘metres’ into kilometres.
(a) 52 m
∵ 1000m = 1km ∴ 1m = \(\frac{1}{1000}\)
or 52 m = 52 x \(\frac{1}{1000}\) km = 0.052 km

(b) 340m
∵ 1m = \(\frac{1}{1000}\) km
∴ 340m = 340 x \(\frac{1}{1000}\) km
= \(\frac{340}{1000}\) km = 3.40 km

(c) 2008m
∵ 1 m = \(\frac{1}{1000}\) km
∴ 2008m = 2008 x \(\frac{1}{1000}\) km = \(\begin{aligned}
&2008 \\
&\hline 1000
\end{aligned}\) km

= (2 + 0.008) km = 2.008 km

Question 4.
Can you now write 52 m as ‘km’ using decimals? How will you write 340 m as ‘km’ using decimals?
Answer:
1000g = 1kg
∴ 1 g = \(\frac{1}{1000}\)kg
∴ 456g = \(\frac{1}{1000}\) x 456kg
= \(\frac{456}{1000}\) kg = 0.456kg

Question 5.
How will you write 2 kg 9 g in kg’ using decimals?
Answer:
2kg9g = 2kg + 9g
= 2kg + (9 x
= (2 + \(\frac{9}{1000}\))
= (2 + 0.009) kg = 2.009 kg

NCERT In-text Question Page No. 178

Question 1.
Find
(i) 0.29 + 0.36
(ii) 0.7 + 0.08
(iii) 1.54 + 1.80
(iv) 2.66 + 1.85
Answer:
(i) 0.29 + 0.36

∵ (9 + 6) hundredths =15 hundredths = 1
tenths + 5 hundredths
Thus, 0.29 + 0.36 = 0.65

(ii) 0.7 + 0.08

Thus, 0.7 + 0.08 = 0.78

(iii) 1.54 + 1.80

Thus, 1.54 + 1.80 = 3.34
Note: 5 tenths + 8 tenths =13 tenths
and 13 tenths = 10 tenths + 3 tenths = 1 one + 3 tenths

(iv) 2.66 + 1.85

Thus, 2.66 + 1.85 = 4.51

NCERT In-text Question Page No. 180

Question 1.
Subtract 1.85 from 5.46
Answer:
1.85 and 5.46 are ‘like decimals’.

Here, 1 is borrowed from ‘ones’ and given to tenths such that:
4 tenths + 10 tenths =14 tenths
5 ones – 1 one = 4 ones

Question 2.
Subtract 5.25 from 8.28
Answer:
5.25 and 8.28 are ‘like decimals’.

Question 3.
Subtract 0.95 from 2.29
Answer:
0.95 and 2.29 are ‘like decimals’.

Question 4.
Subtract 2.25 from 5.68
Answer:
2.25 and 5.68 are ‘like decimals’.