# Tenths and Hundredths

## Overview
In this chapter, students explore decimal numbers through familiar measurements—length in centimetres and millimetres, money in rupees and paise, and temperature in degrees Celsius. The concepts of tenths (0.1) and hundredths (0.01) are reinforced using visual activities, currency conversion, and estimation challenges.

## Key Topics Covered

### 1. Understanding Tenths and Hundredths
- A centimetre is divided into 10 equal parts; each part is **1 millimetre** or **0.1 cm**.
- **0.1 cm** is read as "zero point one centimetre."
- **1 millimetre = 0.1 cm** and **1 centimetre = 10 millimetres**.
- **0.9 cm = 9 mm**, showing 9 tenths of a centimetre.

### 2. Comparing and Estimating Length
- Activities like measuring pencils, ladyfinger, rods, and objects using a scale.
- Practice estimating and then verifying actual length using a ruler.
- Differentiating objects shorter than 1 cm or between 3 cm and 4 cm.

### 3. Guess, Draw, and Measure
- Encourages students to draw and then measure:
- An ant (less than 1 cm)
- A pencil (~7 cm)
- A water-filled glass (5 cm water in 11 cm glass)
- A bangle (20 cm perimeter)
- A curly hair (16 cm)

### 4. Confusing Visual Perception
- Comparison of lines A vs. B and C vs. D to highlight optical illusions.
- Actual measurement resolves confusion, reinforcing the use of scales.

### 5. Use of Decimal in Money
- **1 Rupee = 100 Paise**, hence:
- 10 paise = 0.10 rupee
- 25 paise = 0.25 rupee
- 50 paise = 0.50 rupee
- 99 paise = 0.99 rupee
- Prices shown with decimals (e.g., ₹32.99) and tricks used in pricing (e.g., 1 paisa less).

### 6. Design and Colouring Using Fractions and Decimals
- Colour fractions like **1/10 = 0.1**, **10/100 = 0.10**, **15/100 = 0.15** of a sheet.
- Understanding how **0.10 = 0.1** by colouring different strips.

### 7. Sports Day – Measurement in Metres and Centimetres
- Long jump distances recorded in decimals (e.g., 3.50 m = 3 m and 50 cm).
- Reinforces 1 metre = 100 centimetres → 1 cm = 0.01 m.

### 8. Currency Conversion and Foreign Exchange
- Table of exchange rates of different currencies in Indian rupees.
- Practical applications:
- Converting 1000 Dirham and 2000 Sri Lankan Rupees to INR.
- Spending foreign currency and calculating change in rupees.
- Matching decimal values to corresponding currency denominations.


### 9. Temperature and Decimal Values
- Temperatures of cities shown in decimals (e.g., Mumbai 35.1°C, Srinagar 8.1°C).
- Differences in temperatures are calculated using subtraction of decimal numbers.
- Example: Chennai (29.9°C) – Kolkata (26.6°C) = 3.3°C.
- Understanding rise or drop in temperature in decimals (e.g., 2.5°C increase to reach 40°C).

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## New Terms and Simple Definitions

| Term | Definition |
|-------------------|---------------------------------------------------------------------------|
| Decimal | A number written with a dot (.) to show parts of a whole. For example: 0.5 |
| Tenth | One part out of 10 equal parts. Written as 0.1 |
| Hundredth | One part out of 100 equal parts. Written as 0.01 |
| Millimetre (mm) | A small unit of length. 10 mm = 1 cm |
| Centimetre (cm) | A unit to measure length. 1 cm = 10 mm |
| Metre (m) | A big unit to measure length. 1 m = 100 cm |
| Rupee | Indian currency unit |
| Paisa | Smaller currency unit. 100 paise = 1 rupee |
| Currency | The system of money used in a country |
| Temperature | A measure of hotness or coldness, usually in °C (Celsius) |

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## Practice Problems

### Easy (3)

1. **Convert 0.7 cm to millimetres.**
**Answer**: 0.7 cm = 7 mm

2. **Write 25 paise as a rupee.**
**Answer**: ₹0.25

3. **Which is more: 0.75 or 0.57?**
**Answer**: 0.75 is more than 0.57

### Medium (2)

4. **A frog is 0.9 cm long. How many frogs can sit in a 9 cm line?**
**Answer**: 9 ÷ 0.9 = 10 frogs

5. **Convert 3.5 m into cm.**
**Answer**: 3.5 m = 350 cm

### Difficult (3)

6. **Find the difference: 29.9°C (Chennai) – 26.6°C (Kolkata)**
**Answer**: 3.3°C

7. **If 99 paise = ₹0.99, what is ₹3.99 in paise?**
**Answer**: 399 paise

8. **You bought 3 items costing ₹2.50, ₹3.75 and ₹4.25. What is the total cost?**
**Answer**: ₹2.50 + ₹3.75 + ₹4.25 = ₹10.50

### Very Difficult (2)

9. **If 1 pen costs ₹4.75, how much will 3 pens cost?**
**Answer**: ₹4.75 × 3 = ₹14.25

10. **A person has ₹500. He changes it into Hong Kong dollars. 1 HKD = ₹5.10. How many HKD will he get?**
**Answer**: ₹500 ÷ 5.10 ≈ 98.04 HKD

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