## Decimals Exercise – 8.1

**Question 1. Which is greater?**

**0.3 or 0.4****0.07 or 0.02****3 or 0.8****0.5 or 0.05****1.23 or 1.2****0.099 or 0.1 9****1.5 or 1.50****1.431 or 1.490****3.3 or 3.300****5.64 or 5.603**

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

- 0.3 <0.4
- 0.07 >0.02
- 3.0 or 0.8⇒ 3.0 > 0.8
- 0.50 or 0.05 ⇒ 0.50 > 0.05
- 1.23 or 1.20 ⇒ 1.23 >1.20
- 0.099 or 0.190 ⇒ 0.099 < 0.190
- 1.50 or 1.50 ⇒ 1.50 = 1.50
- 1.431 < 1.490
- 3.300 or 3.300 ⇒ 3.300 = 3.300
- 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 :

- 1.8 or 1.82
- 1.0009 or 1.09
- 10.01 or 100.1
- 5.1 or 5.01
- 4.213 or 421.3

Before comparing, we write both terms in decimals

- 1.80 or 1.82 ⇒ 1.82 is greater than 1.8
- 1.0009 or 1.0900 ⇒ 1.09 is greater than 1.0009
- 10.01 or 100.10 ⇒ 100.1 is greater than 10.01
- 5.10 or 5.01 ⇒ 5.1 is greater than 5.01
- 4.213 or 421.300 ⇒ 421.3 is greater than 4.213

## Decimals Exercise – 8.2

**1. Express as rupees using decimals.**

**5 paise****75 paise****20 paise****50 rupees 90 paise****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.**

**15 cm****6 cm****2 m 45 cm****9 m 7 cm****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 \(=\frac{1}{100} \times 419 \mathrm{~m}=\frac{419}{100}=4.19 \mathrm{~m}\)

**Question 3. Express as cm using decimals.**

**5 mm****60 mm****164 mm****9 cm 8 mm****93 mm****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.**

**8 m****88 m****8888 m****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.**

**2 g****100 g****3750 g****5 kg 8 g****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:**

**0.007 + 8.5 + 30.08****15 + 0.632 + 13.8****27.076 + 0.55 + 0.004****25.65 + 9.005 + 3.7****0.75 + 10.425 + 2****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:**

**₹ 18.25 from ₹ 20.75****202.54 m from 250 m****₹ 5.36 from ₹ 8.40****2.051 km from 5.206 km****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:**

**9.756-6.28****21.05-15.27****18.5-6.79****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.