# Large Numbers Around Us

## Overview

In this chapter, students explore the concept of large numbers—how to read, write, estimate, and operate with them. Through relatable contexts like rice varieties, city populations, heights of buildings, and thought experiments, learners understand place values in Indian and International systems. The chapter integrates numerical reasoning, estimation, rounding, comparisons, and real-world data handling with fun mathematical tools like creative calculators and stick puzzles.

## Key Topics Covered

### 1. Understanding One Lakh

- Students learn what one lakh (1,00,000) means in numerical terms and real-life context.
- Estimating how many rice varieties one can taste in a lifetime introduces daily life connections.
- Discussion prompts include population comparisons and lifespan estimates.

### 2. Place Value and Number Naming

- Numbers are named using the **Indian Place Value System**: Thousand, Lakh, Crore.
- Introduction to using commas for readability.
- Comparison with **International (American) System**: Thousand, Million, Billion.

**Examples**:

- 3,00,600 = Three lakh six hundred (Indian), 300,600 = Three hundred thousand six hundred (International)

### 3. Creative Use of Calculators

- Introduction to imaginary calculators like:

- **Thoughtful Thousands** (+1000 only)
- **Tedious Tens** (+10 only)
- **Handy Hundreds** (+100 only)
- **Creative Chitti** (uses all place value buttons creatively)
- **Systematic Sippy** (minimizes button clicks)

**Concepts Reinforced**:

- Multiples and counting
- Decomposition and recomposition of numbers
- Efficient methods of reaching large numbers with fewer operations

### 4. Comparing and Visualising Large Numbers

- Comparing heights like Somu’s building, Statue of Unity, and waterfalls.
- Thinking if one lakh is "large" or "small" based on different contexts (number of hairs, stadium capacity, etc.).
- Concept of rounding large numbers to nearest thousand, lakh, or crore.

**Examples**:

- 6,72,85,183 rounded to:

- Nearest thousand: 6,72,85,000
- Nearest crore: 7,00,00,000

### 5. Estimation and Approximation

- Emphasis on estimating sums and differences for quicker calculations and understanding scale.
- Rounded values used in real-world scenarios (e.g., sweets for a school, shop pricing).
- Distinction between **exact values**, **rounding up**, and **rounding down**.

**Examples**:

- Estimating 4,63,128 + 4,19,682 ≈ 8,82,810
- Estimating 14,63,128 − 4,90,020 ≈ 9,73,108

### 6. Data Interpretation from Population Tables

- Population growth comparison between 2001 and 2011 for Indian cities.
- Students infer approximate differences and observe trends in urban expansion.
- Questions based on approximation and multiplication for scale comparison.

### 7. Patterns in Multiplication

- Exploring shortcut methods for multiplication:

- Multiply by 5 as (number × 10) ÷ 2
- Multiply by 25 as (number × 100) ÷ 4

- Identifying patterns in multiplication (e.g., 111 × 111, 66 × 61)

**Examples**:

- 2500 × 12 = 30,000
- 25 × 12 = 300

### 8. Exploring Large Number Facts

- Real-world data brings alive large number operations:

- Distance to the Sun = 2100 × 70,000
- Weight of global plastic = 52,00,00,00,000 ÷ 130
- Number of kīrtanas by Purandaradāsa = 1250 × 380

### 9. Fun With Large Numbers

- Puzzles and riddles involving combinations, digit counts, card use, and estimation.
- “Toothpick digits” challenge using matchsticks to form numbers.
- Logical thinking activities (e.g., how many coins equal the height of the Statue of Unity)

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## New Terms and Simple Definitions

| Term | Definition |
| ------------- | -------------------------------------------------------------- |
| Lakh (लाख) | 1,00,000 (one hundred thousand) |
| Crore (करोड़) | 1,00,00,000 (ten million) |
| Arab (अरब) | 1,00,00,00,000 (one billion) |
| Estimate | An approximate value |
| Round off | Making a number simpler but close to the original |
| Place Value | The value of a digit based on its position in the number |
| Digit | A single numeral (0–9) |
| Population | The total number of people in a place |
| Approximation | A value that is close enough to the correct answer |
| Comma Usage | Helps in reading big numbers in Indian or International system |

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## Practice Problems

### Easy (3)

1. Write the number name of 5,43,210 in the Indian system.
**Answer**: Five lakh forty-three thousand two hundred ten.

2. What is the value of 25 × 100?
**Answer**: 2500

3. Round off 3,47,890 to the nearest lakh.
**Answer**: 3,00,000

### Medium (2)

4. Write the number 23,45,001 in words in the International system.
**Answer**: Two million three hundred forty-five thousand one.

5. Estimate the sum of 6,89,423 and 3,10,550 by rounding to the nearest lakh.
**Answer**: 7,00,000 + 3,00,000 = 10,00,000

### Difficult (3)

6. If one bus holds 50 people, how many buses are needed for 1,25,000 people?
**Answer**: 1,25,000 ÷ 50 = 2500 buses

7. A number is rounded to 8,00,000. It lies between which two numbers?
**Answer**: Between 7,50,000 and 8,49,999

8. Multiply 125 × 40 × 8 × 25 using shortcuts.
**Answer**:
125 × 8 = 1000
40 × 25 = 1000
So, 1000 × 1000 = 10,00,000

### Very Difficult (2)

9. A train covers 13,95,000 km in 150 days. What is the average distance per day?
**Answer**: 13,95,000 ÷ 150 = 9300 km/day

10. How many zeros are there in 1 billion? How is it written in Indian system?
**Answer**: 9 zeros. 1 billion = 100 crore = 1,00,00,00,000

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