Chapter 1 — Large Numbers Around Us

Ganita Prakash • Grade 7 • Part I • 2026–27

🌍 Why do we need very large numbers?

Population, money, distances, visitors to a website and quantities of materials can quickly become too large to count comfortably in ones or thousands. This chapter develops number sense: not just reading a large number, but understanding its size, choosing an appropriate unit, comparing it and deciding when an exact value is necessary.

1. Place-value systems

The value does not change when we change the naming system. Only the grouping and names change. In the Indian system, digits are grouped as 3 digits from the right and then in pairs; in the International system, digits are grouped in sets of three.

2. Reading a large number correctly

Consider 7,08,45,321. From right to left the places are ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs and crores. Therefore it is read as seven crore eight lakh forty-five thousand three hundred twenty-one.

3. Exact value vs approximate value

Exact: the actual number, such as 4,96,482 people. Approximate: a nearby value useful for quick communication, such as about 5 lakh people.

When rounding, inspect the digit immediately after the place you want. A digit 5–9 increases the retained digit by 1; 0–4 leaves it unchanged.

4. Estimation is a mathematical decision

If a school has 1,987 students, saying “about 2,000” is useful when estimating buses or chairs. But for preparing individual report cards, the exact number is necessary. Good mathematics includes deciding how much accuracy the situation needs.

🧠 Worked examples

1. Convert 3 crore to millions: 1 crore = 10 million, so 3 crore = 30 million.
2. Round 8,64,29,701 to nearest crore: look at the lakh part, 64 lakh. Since it is at least 50 lakh, the answer is 9 crore.
3. Compare 5,08,00,000 and 48,000,000: 5,08,00,000 = 50.8 million, so it is greater than 48 million.

🎯 Explore & Discuss

1. Which is larger: 99 lakh or 9.9 million? Explain without a calculator.
2. Find a quantity in your surroundings that is best described approximately rather than exactly. Why?
3. Make a number between 4 crore and 5 crore that rounds to 5 crore.

🧩 Concept MCQs

1. 1 crore is equal to: A. 1 million B. 10 million C. 100 million D. 1 billion
2. In 6,42,18,305, the value of 2 is: A. 2,000 B. 20,000 C. 2,00,000 D. 20,00,000
3. 7,49,999 rounded to nearest lakh is: A. 7,00,000 B. 7,50,000 C. 8,00,000 D. 70,000
4. Which situation needs an exact number? A. estimating crowd size B. deciding approximate distance C. recording a student’s marks D. estimating chairs

Answers: 1-B, 2-C, 3-C, 4-C

📌 Case-based Challenge

A district has a population of 48,72,650. A report says “approximately 49 lakh.”

1. Why is the approximation reasonable?
2. Write the exact population in words.
3. Express the population approximately in millions.
4. Give one situation where the exact figure should be used instead.

📝 Practice Worksheet

1. Write 9,04,07,016 in words.
2. Convert 7 crore into millions.
3. Round 6,74,82,119 to the nearest crore.
4. Compare 8.2 million and 82 lakh.
5. Create two numbers that round to 12 crore to the nearest crore.

🔁 Quick Revision

Remember: place value → Indian/International grouping → exact and approximate values → rounding → estimation → choosing suitable accuracy.

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