## Things to remember...

- To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One block divided into 10 equal parts means each part is 1/10 (one-tenth) of a unit. It can be written as 0.1 in decimal notation. The dot represents the decimal point and it comes between the units place and the tenths place.
- Every fraction with denominator 10 can be written in decimal notation and vice-versa.
- One block divided into 100 equal parts means each part is (1/100) (one-hundredth) of a unit. It can be written as 0.01 in decimal notation.
- Every fraction with denominator 100 can be written in decimal notation and vice-versa.
- In the place value table, as we go from left to the right, the multiplying factor becomes 1/10 of the previous factor.
- The place value table can be further extended from hundredths to 1/10 of hundredths i.e. thousandths (1/1000), which is written as 0.001 in decimal notation.
- All decimals can also be represented on a number line.
- Every decimal can be written as a fraction.
- Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole parts are equal then the tenth parts can be compared and so on.
- Decimals are used in many ways in our lives. For example, in representing units of money, length and weight.

**1. Subtract : (a) Rs 18.25 from Rs 20.75 (b) 202.54 m from 250 m (c) Rs 5.36 from Rs 8.40 (d) 2.051 km from 5.206 km (e) 0.314 kg from 2.107 kg**

**Answer:**(a) Rs 18.25 from Rs 20.75

Tens | Ones | Tenths | Hundredths |

2 | 0 | 7 | 5 |

1 | 8 | 2 | 5 |

0 | 2 | 5 | 0 |

Rs.2.50 |

Hundreds | Tnes | Ones | Tenths | Hundredths |

2 | 5 | 0 | 0 | 0 |

2 | 0 | 2 | 5 | 4 |

0 | 4 | 7 | 4 | 6 |

47.46 m |

Ones | Tenths | Hundredths |

8 | 4 | 0 |

5 | 3 | 6 |

3 | 0 | 4 |

Rs.3.04 |

Tens | Ones | Tenths | Hundredths |

5 | 2 | 0 | 6 |

2 | 0 | 5 | 1 |

3 | 1 | 5 | 5 |

3.155 Km |

Tens | Ones | Tenths | Hundredths |

2 | 1 | 0 | 7 |

0 | 3 | 1 | 4 |

1 | 7 | 9 | 3 |

1.793 Kg |

**2. Find the value of : (a) 9.756 – 6.28 (b) 21.05 – 15.27 (c) 18.5 – 6.79 (d) 11.6 – 9.847**

**Answer:**(a) 9.756 – 6.28

Ones | Tenths | Hundredths | Thosandths |

9 | 7 | 5 | 6 |

6 | 2 | 8 | 0 |

3 | 4 | 7 | 6 |

9.756 – 6.28 = 3.476 |

Ones | Tenths | Hundredths | Thosandths |

2 | 1 | 2 | 5 |

1 | 5 | 0 | 7 |

0 | 5 | 7 | 8 |

21.05 – 15.27 = 5.78 |

Tens | Ones | Tenths | Hundredths |

1 | 8 | 5 | 0 |

0 | 6 | 7 | 9 |

1 | 1 | 7 | 1 |

18.5 – 6.79 = 11.71 |

Tens | Ones | Tenths | Hundredths | Thosandths |

1 | 1 | 6 | 0 | 0 |

0 | 9 | 8 | 4 | 7 |

0 | 1 | 7 | 5 | 3 |

11.6 – 9.847 = 1.753 |

**3. Raju bought a book for Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?**

**Answer:**The money Raju get back from the shopkeeper=Rs50.00 - 35.65

Tens | Ones | Tenths | Hundredths |

5 | 0 | 0 | 0 |

3 | 5 | 6 | 5 |

1 | 4 | 3 | 5 |

∴ Rs50.00 - Rs35.65 =Rs 14.35 |

**Alternatively :**

The total Money Raju gave to shopkeeper | =Rs 50.00 |

The cost of the book | =Rs 35.65 |

The ballance amount after payment | =Rs50.00 - Rs35.65 =Rs 14.35 |

∴The money Raju get back from the shopkeeper | =Rs 14.35 |

**4. Rani had Rs 18.50. She bought one ice-cream for Rs 11.75. How much money does she have now?**

**Answer:**The money, Rani have now=Rs 18.50 - Rs 11.75

Tens | Ones | Tenths | Hundredths |

1 | 8 | 5 | 0 |

1 | 1 | 7 | 5 |

0 | 6 | 7 | 5 |

∴ Rs 18.50 - Rs 11.75 =Rs 6.75 |

**Alternatively :**

The total Money Rani had | =Rs 18.50 |

The price of Ice Cream she bought | =Rs 11.75 |

The ballance amount after payment of Ice-Cream | =Rs 18.50 - Rs 11.75 |

=Rs 6.75 | |

∴The money Rani she have now | =Rs 6.75 |

**5. Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?**

**Answer:**

The total length of the cloth, Tina had | = 20 m 5 cm |

= 20.05 m | |

The length of the cloth, Tina had cut for curtain | = 4m 50cm |

4.50 m | |

The remaining length of cloth | = 20.05m - 4.50 m |

= 15.55 m | |

∴The lenth of the cloth left with her now | = 15.55 m OR |

= 15m 55cm |

**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?**

**Answer:**

The total distance Namita travels every day | = 20 Km 50m |

= 20.05 Km | |

The distance which she travels by bus | = 10km 200m |

= 10.2 Km | |

The rest of the distance | = 20.05km - 10.2km |

= 9.85km | |

∴The distance which Namita travels by auto | = 9.85km OR 9km 850m |

**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?**

**Answer:**

The total weight of vegitables, Aakash bought | = 10kg |

The weight of Onions | = 3kg 500g |

= 3.5 kg | |

The weight of Tomatoes | = 2kg 75g |

= 2.075 kg | |

The weight of Potatoes | = 10kg - (2.075kg +3.5 kg kg) |

= 10kg - 5.575 kg | |

= 4.425kg | |

∴The weight of the potatoes | = 4.425kg OR 4 Kg 425 g |

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