CBSE Solutions For Class 6 Maths Chapter 8 Decimals

Decimals Exercise – 8.1

Question 1. Which is greater?

  1. 0.3 or 0.4
  2. 0.07 or 0.02
  3. 3 or 0.8
  4. 0.5 or 0.05
  5. 1.23 or 1.2
  6. 0.099 or 0.1 9
  7. 1.5 or 1.50
  8. 1.431 or 1.490
  9. 3.3 or 3.300
  10. 5.64 or 5.603

Solution: Before comparing, we write both terms in like decimals:

  1. 0.3 <0.4
  2. 0.07 >0.02
  3. 3.0 or 0.8⇒ 3.0 > 0.8
  4. 0.50 or 0.05 ⇒ 0.50 > 0.05
  5. 1.23 or 1.20 ⇒ 1.23 >1.20
  6. 0.099 or 0.190 ⇒ 0.099 < 0.190
  7. 1.50 or 1.50 ⇒ 1.50 = 1.50
  8. 1.431 < 1.490
  9. 3.300 or 3.300 ⇒ 3.300 = 3.300
  10. 5.640 or 5.603 ⇒ 5.640 >5.603

Question 2. Make five more examples and find the greater number from them.
Solution: Five examples are :

  1. 1.8 or 1.82
  2. 1.0009 or 1.09
  3. 10.01 or 100.1
  4. 5.1 or 5.01
  5. 4.213 or 421.3

Before comparing, we write both terms in decimals

  1. 1.80 or 1.82 ⇒ 1.82 is greater than 1.8
  2. 1.0009 or 1.0900 ⇒ 1.09 is greater than 1.0009
  3. 10.01 or 100.10 ⇒ 100.1 is greater than 10.01
  4. 5.10 or 5.01 ⇒ 5.1 is greater than 5.01
  5. 4.213 or 421.300 ⇒ 421.3 is greater than 4.213

Decimals Exercise – 8.2

1. Express as rupees using decimals.

  1. 5 paise
  2. 75 paise
  3. 20 paise
  4. 50 rupees 90 paise
  5. 725 paise

Solution:

1 paisa \(=₹ \frac{1}{100}\)

5 paise \(=₹\left(\frac{1}{100} \times 5\right)=₹ 0.05\)

1 paisa \(=₹ \frac{1}{100}\)

75 paise \(=₹\left(\frac{1}{100} \times 75\right)=₹ 0.75\)

1 paisa \(=₹ \frac{1}{100}\)

20 paise \(=₹\left(\frac{1}{100} \times 20\right)=₹ 0.20\)

1 paisa \(=₹ \frac{1}{100}\)

₹ 50 + 90 paise \(=₹\left(50+\frac{1}{100} \times 90\right)\)

= ₹ 50.90

1 paisa \(=₹ \frac{1}{100}\)

725 paise \(=₹\left(\frac{1}{100} \times 725\right)=\frac{725}{100}=₹ 7.25\)

Question 2. Express as metres using decimals.

  1. 15 cm
  2. 6 cm
  3. 2 m 45 cm
  4. 9 m 7 cm
  5. 419 cm

Solution:

1 cm \(=\frac{1}{100} \mathrm{~m}\)

15 cm \(=\frac{1}{100} \times 15 \mathrm{~m}=0.15 \mathrm{~m}\)

1 cm \(=\frac{1}{100} \mathrm{~m}\)

6 cm \(=\frac{1}{100} \times 6 \mathrm{~m}=0.06 \mathrm{~m}\)

1 cm \(=\frac{1}{100} \mathrm{~m}\)

2 m 45 cm \(2 \mathrm{~m} 45 \mathrm{~cm}=\left(2+\frac{1}{100} \times 45\right) \mathrm{m}=2.45 \mathrm{~m}\)

1 cm \(=\frac{1}{100} \mathrm{~m}\)

9 m 7 cm \(=\left(9+\frac{1}{100} \times 7\right) \mathrm{m}=9.07 \mathrm{~m}\)

1 cm \(=\frac{1}{100} \mathrm{~m}\)

419 cm \(=\frac{1}{100} \times 419 \mathrm{~m}=\frac{419}{100}=4.19 \mathrm{~m}\)

CBSE Solutions Class 6 Maths Chapter 8 Decimals

Question 3. Express as cm using decimals.

  1. 5 mm
  2. 60 mm
  3. 164 mm
  4. 9 cm 8 mm
  5. 93 mm
  6. Solution:

1 mm \(=\frac{1}{10} \mathrm{~cm}\)

5 mm \(=\frac{1}{10} \times 5 \mathrm{~cm}=0.5 \mathrm{~cm}\)

1 mm \(=\frac{1}{10} \mathrm{~cm}\)

60 mm \(=\frac{1}{10} \times 60 \mathrm{~cm}=6 \mathrm{~cm}\)

1 mm \(=\frac{1}{10} \mathrm{~cm}\)

164 mm \(=\frac{1}{10} \times 164 \mathrm{~cm}=16.4 \mathrm{~cm}\)

1 mm \(=\frac{1}{10} \mathrm{~cm}\)

9 cm 8 mm \(=\left(9+\frac{1}{10} \times 8\right) \mathrm{cm}=9.8 \mathrm{~cm}\)

1 mm \(=\frac{1}{10} \mathrm{~cm}\)

93 mm \(=\frac{1}{10} \times 93 \mathrm{~cm}=9.3 \mathrm{~cm}\)

Question 4. Express as km using decimals.

  1. 8 m
  2. 88 m
  3. 8888 m
  4. 70 km 5 m

Solution:

1 m \(=\frac{1}{1000} \mathrm{~km}\)

8 m \(=\frac{1}{1000} \times 8 \mathrm{~km}=0.008 \mathrm{~km}\)

1 m \(=\frac{1}{1000} \mathrm{~km}\)

88 m\(=\frac{1}{1000} \times 88 \mathrm{~km}=0.088 \mathrm{~km}\)

1 m \(=\frac{1}{1000} \mathrm{~km}\)

8888 m \(=\frac{1}{1000} \times 8888 \mathrm{~km}=8.888 \mathrm{~km}\)

1 m \(=\frac{1}{1000} \mathrm{~km}\)

70 km 5 m \(=\left(70+\frac{1}{1000} \times 5\right) \mathrm{km}=70.005 \mathrm{~km}\)

Question 5. Express as kg using decimals.

  1. 2 g
  2. 100 g
  3. 3750 g
  4. 5 kg 8 g
  5. 26 kg 50 g

Solution:

1 g \(=\frac{1}{1000} \mathrm{~kg}\)

2 g \(=\frac{1}{1000} \times 2 \mathrm{~kg}=0.002 \mathrm{~kg}\)

1 g \(=\frac{1}{1000} \mathrm{~kg}\)

100 g \(=\frac{1}{1000} \times 100 \mathrm{~kg}=0.1 \mathrm{~kg}\)

1 g \(=\frac{1}{1000} \mathrm{~kg}\)

3750 g \(=\frac{1}{1000} \times 3750 \mathrm{~kg}=3.750 \mathrm{~kg}\)

1 g \(=\frac{1}{1000} \mathrm{~kg}\)

5 kg 8 g \(=\left(5+\frac{1}{1000} \times 8\right) \mathrm{kg}=5.008 \mathrm{~kg}\)

1 g \(=\frac{1}{1000} \mathrm{~kg}\)

26 kg 50 g \(=\left(26+\frac{1}{1000} \times 50\right) \mathrm{kg}=26.050 \mathrm{~kg}\)

Decimals Exercise – 8.3

Question 1. Find the sum in each of the following:

  1. 0.007 + 8.5 + 30.08
  2. 15 + 0.632 + 13.8
  3. 27.076 + 0.55 + 0.004
  4. 25.65 + 9.005 + 3.7
  5. 0.75 + 10.425 + 2
  6. 280.69 + 25.2 + 38

Solution:

1. \(\begin{array}{r}
0.007 \\
8.500 \\
+30.080 \\
\hline 38.587 \\
\hline
\end{array}\)

2. \(+\begin{array}{r}
15.000 \\
0.632 \\
13.800 \\
\hline 29.432 \\
\hline
\end{array}\)

3. \(\begin{array}{r}
27.076 \\
0.550 \\
+0.004 \\
\hline \underline{27.630} \\
\hline
\end{array}\)

4. \(\begin{array}{r}
25.650 \\
9.005 \\
+3.700 \\
\hline 38.355 \\
\hline
\end{array}\)

5. \(\begin{array}{r}
0.750 \\
10.425 \\
+2.000 \\
\hline 13.175 \\
\hline
\end{array}\)

6. \(\begin{array}{r}
280.69 \\
25.20 \\
+38.00 \\
\hline 343.89 \\
\hline
\end{array}\)

Question 2. Rashid spent ₹ 35.75 for the Maths book and ₹ 32.60 for the Science book. Find the total amount spent by Rashid.
Solution:

Money spent formats books =₹ 35.75

Money spent on Science book = ₹ 32.60

Total money spent = ₹ 35.75 + ? 32.60 = ₹ 68.35

Therefore, the total money spent by Rashid is ₹ 68.35

Question 3. Radhika’s mother gave her ₹ 10.50 and her father gave her ₹ 1 5.80, find the total amount given to Radhika by the parents.
Solution:

Money given by mother = ₹ 10.50

Money given by father ₹ 15.80

Total money received by Radhika = ₹ 10.50 + ₹ 15.80 = ₹ 26.30

Therefore, the total money received by Radhika is ₹ 26.30

Question 4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of clothes bought by her.
Solution:

Cloth bought for shirt = 3 m 20 cm = 3.20 m

Cloth bought for trouser = 2 m 5 cm = 2.05 m

Total length of cloth bought by Nasreen = 3.20 m + 2.05 m = 5.25 m

Therefore, the total length of cloth bought by Nasreen is 5.25 m

Question 5. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he walk in all?
Solution:

Distance travelled in the morning = 2 km 35 m = 2.035 km

Distance travelled in the evening =1 km 7m = 1.007 km

Total distance travelled = (2.035 + 1.007) km- 3.042 km

Therefore, the total distance travelled by Naresh is 3.042 km.

Question 6. Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot to reach her school. How far is her school from her residence?
Solution:

Distance travelled by bus = 15 km 268 m = 15.268 km

Distance travelled by car = 7 km 7m = 7.007 km

Distance travelled on foot = 500 m = 0.500 km

Total distance travelled = (15.268 + 7.007 + 0.500) km = 22.775 km

Therefore, the total distance travelled by Sunita is 22.775 km

Question 7. Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850g flour. Find the total weight of his purchases.
Solution:

Weight of Rice = 5 kg 400 g = 5.400 kg

Weight of Sugar = 2 kg 20 g = 2.020 kg

Weight flour = 10 kg 850 g = 10.850 kg

Total weight = (5.400 + 2.020 + 10.850) kg = 18.270 kg

Therefore, the total weight of Ravi’s purchases is 18.270 kg

Decimals Exercise – 8.4

Question 1. Subtract:

  1. ₹ 18.25 from ₹ 20.75
  2. 202.54 m from 250 m
  3. ₹ 5.36 from ₹ 8.40
  4. 2.051 km from 5.206 km
  5. 0.314 kg from 2.107 kg

Solution:

1. \(\begin{array}{r}
20.75 \\
-18.25 \\
\hline 02.50 \\
\hline
\end{array}\)

₹ 20.75- ₹ 18.25 2.50

2. \(\begin{array}{r}
250.00 \\
-202.54 \\
\hline 47.46 \\
\hline
\end{array}\)

250 m- 202.54 m = 47.46 m

3. \(\begin{array}{r}
8.40 \\
-5.36 \\
\hline 3.04 \\
\hline
\end{array}\)

₹ 8.40 – ₹ 5.36 = ? 3.04

4. \(\begin{array}{r}
5.206 \\
-2.051 \\
\hline 3.155 \\
\hline
\end{array}\)

5.206 km- 2.051 km = 3.155 km

5. \(\begin{array}{r}
2.107 \\
-0.314 \\
\hline 1.793
\end{array}\)

2.107 kg – 0.314 kg = 1.793 kg

Question 2. Find the value of:

  1. 9.756-6.28
  2. 21.05-15.27
  3. 18.5-6.79
  4. 11.6-9.847

Solution:

1. \(\begin{array}{r}
9.756 \\
-6.28 \\
\hline 3.476 \\
\hline
\end{array}\)

2. \(\begin{array}{r}
21.05 \\
-15.27 \\
\hline 05.78 \\
\hline
\end{array}\)

3. \(\begin{array}{r}
18.50 \\
-6.79 \\
\hline 11.71 \\
\hline
\end{array}\)

4. \(\begin{array}{r}
11.600 \\
-9.847 \\
\hline 1.753 \\
\hline
\end{array}\)

Question 3. Raju bought a book for ₹ 35.65. He gave ₹ 50 to the shopkeeper. How much money did he get back from the shopkeeper?
Solution:

The total amount is given to shopkeeper=₹ 50

Cost of book = ₹ 35.65

Amount left = ₹ 50.00- ₹ 35.65 = ₹ 14.35

Therefore, Raju got back ₹ 14.35 from the shopkeeper.

Question 4. Rani had ₹ 18.50. She bought one ice cream for ₹ 1 1.75. How much money does she have now?
Solution:

Total money = ₹ 18.50

Cost of ice-cream = ₹ 11.75

Amount left = ₹ 18.50- ₹ 11.75 = ₹ 6.75

Therefore, Rani has ₹ 6.75 now

Question 5. Tina had 20 m 5 cm long cloth. She cuts 4m 50 cm length of cloth from this for making a curtain. How many clothes are left with her?
Solution:

Total length of cloth = 20 m 5 cm = 20.05 m

Length of cloth used = 4 m 50 cm = 4.50 m

Remaining cloth = 20.05 m- 4.50 m = 15.55 m

Therefore, 15.55 m of cloth is left with Tina

Question 6. Namita travels 20 km 50 m every day. Out of this, she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?
Solution:

Total Distance travelled = 20 km 50 m

= 20.050 km

Distance travelled by auto = (20.050- 10.200) km = 9.850 km

Therefore, 9.850 km distance is travelled by auto.

Question 7. Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
Solution:

Weight of onions=3kg 500 g = 3.500kg

Weight of tomatoes = 2 kg 75 g = 2.075 kg

Total weight of onions and tomatoes = (3.500 + 2.075) kg = 5.575 kg

Therefore, weight of potatoes = (10.000- 5.575) kg = 4.425 kg

Thus, the weight of potatoes is 4.425 kg.

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