Large Numbers Around Us - Class 7 Mathematics (CBSE)

Based on the 2026-27 Class 7 Mathematics sequence for NCERT Ganita Prakash. These notes are written for students: understand the idea first, then practise enough examples to become accurate.

1. Why this chapter matters

Class 7 begins by zooming out from school-level numbers to numbers used in newspapers, budgets, populations, distances, and digital data. The chapter is less about memorising long names and more about seeing how place value lets us read, compare, estimate, and reason with quantities that are too large to count one by one.

In school tests, this chapter can appear as direct calculations, reasoning questions, short explanations, activity-based questions, and word problems. The safest preparation is not to memorise a single trick, but to know what each idea means and when to use it.

2. Core ideas

Place value is a system, not a list

A digit changes value when its position changes. In 72,45,318, the digit 7 stands for seventy lakh, while the same 7 in 7,245 would stand for seven thousand. This is why commas are helpful: they show groups.

Indian and international systems

The Indian system groups after hundreds as thousands, lakhs, and crores. The international system groups as thousands, millions, and billions. The number 5,23,40,000 is 5 crore 23 lakh 40 thousand in the Indian system and 52,340,000, or 52 million 340 thousand, internationally.

Estimation

An estimate is a sensible nearby value. When planning a budget, checking a calculation, or comparing populations, an estimate often matters more than exact arithmetic. Good students use estimation to catch impossible answers.

3. Rules and formulas to remember

• 1 lakh: 1,00,000. Used in Indian place value for large counts.
• 1 crore: 1,00,00,000. 100 lakhs make 1 crore.
• Expanded form: 72,45,318 = 70,00,000 + 2,00,000 + 40,000 + 5,000 + 300 + 10 + 8. Shows the value of each digit.
• Rounding to nearest thousand: Look at the hundreds digit. If it is 5 or more, increase the thousands digit by 1.

4. Worked examples

Example 1: Write 4,08,52,019 in words.

Group the number as 4 crore | 8 lakh | 52 thousand | 19. So it is four crore eight lakh fifty-two thousand nineteen.

Example 2: Which is larger: 6,75,40,200 or 67,54,020?

Compare by place value. The first number is 6 crore 75 lakh plus, while the second is only 67 lakh plus. Therefore 6,75,40,200 is larger.

Example 3: Estimate 8,97,431 + 2,04,880 to the nearest lakh.

8,97,431 rounds to 9,00,000. 2,04,880 rounds to 2,00,000. Estimated sum = 11,00,000.

Example 4: A stadium has 48,650 seats. About how many seats are in 12 such stadiums?

Round 48,650 to 50,000. Then 50,000 x 12 = 6,00,000. The exact count is near six lakh seats.

5. Activity corner

Take any large number from a news headline, such as a city population or a government budget. Rewrite it in Indian notation, international notation, words, expanded form, and rounded form. This single activity builds most of the chapter.

When writing an activity answer, include three things:

• What you did.
• What you observed.
• What mathematical rule or pattern the activity shows.

6. Common mistakes and how to avoid them

• Mistake: Writing commas after every three digits in the Indian system Fix: Use 3 digits at the end, then groups of 2: 7,24,58,900.
• Mistake: Comparing by the first digit only Fix: First compare number of digits or place-value groups.
• Mistake: Rounding without saying the place Fix: Write whether you rounded to nearest ten, hundred, thousand, lakh, or crore.

7. How to write high-scoring answers

1. State the given information in mathematical form.
2. Write the rule, formula, diagram, table, or operation you are using.
3. Show every step clearly.
4. Keep units such as cm, m, rupees, degrees, or minutes where needed.
5. Check whether the answer is reasonable.

8. Practice set

1. Read 9,07,05,210 in words.
2. Write seventy-two lakh thirty-five thousand six in numerals.
3. Round 38,76,420 to the nearest lakh.
4. Find the difference between 1 crore and 75 lakh.
5. Form the greatest 7-digit number using 0, 1, 2, 5, 7, 8, 9 once.
6. Why is estimation useful before multiplying large numbers?

9. Answer key

1. Read 9,07,05,210 in words. Answer: Nine crore seven lakh five thousand two hundred ten.

2. Write seventy-two lakh thirty-five thousand six in numerals. Answer: 72,35,006.

3. Round 38,76,420 to the nearest lakh. Answer: 39,00,000.

4. Find the difference between 1 crore and 75 lakh. Answer: 25 lakh.

5. Form the greatest 7-digit number using 0, 1, 2, 5, 7, 8, 9 once. Answer: 98,75,210.

6. Why is estimation useful before multiplying large numbers? Answer: It helps check whether the final answer is reasonable.

10. Quick revision

• Main themes: large whole numbers, Indian and international place value, estimation, number patterns.
• Redo the worked examples without looking at the solutions.
• Explain the activity in your own words.
• Correct the common mistakes once before the test.
• Create one new word problem from daily life and solve it step by step.