Chapter focus
Large numbers describe populations, distances, budgets and other quantities beyond everyday counting. Place-value systems let us read and compare them without inventing a new symbol for every value.
These original explanations and practice support revision. Use the complete activities and examples in your assigned Ganita Prakash Part I.
1. Place value in the Indian system
In the Indian system, the first comma is placed after three digits from the right; after that, commas separate groups of two digits. The places from right to left are ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs, crores, ten-crores and so on.
Read 7,34,25,618 as seven crore thirty-four lakh twenty-five thousand six hundred eighteen. Expand it by place value:
7,34,25,618 = 7 crore + 34 lakh + 25 thousand + 618.
Zero holds an empty place. In 5,06,204, the zero indicates no ten-thousands and no tens; removing it changes the value.
2. Place value in the international system
The international system groups digits in threes from the right: ones, thousands, millions, billions and so on. The same quantity 7,34,25,618 is written 73,425,618 and read as seventy-three million four hundred twenty-five thousand six hundred eighteen.
1,000 = 103
1,00,000 = 100,000 = 100 thousand
1,000,000 = 10 lakh
1,00,00,000 = 10,000,000 = 10 million
1,000,000,000 = 100 crore
Comma placement changes with the naming convention, but the number’s value does not.
3. Compare and order large numbers
First compare the number of digits. A number with more digits is greater when both are positive whole numbers. If the digit counts match, compare from the leftmost digit and stop at the first place where they differ.
Worked example: compare 8,45,30,900 and 8,54,03,900
- Both have the same number of digits and 8 crores.
- Compare the lakh group: 45 lakh is less than 54 lakh.
- Therefore 8,45,30,900 < 8,54,03,900.
Write numbers in the same system before comparing their comma groups.
4. Estimate by rounding
Rounding gives a nearby value that is easier to use mentally. To round to a chosen place, look at the digit immediately to its right: if it is 5 or more, increase the chosen digit by one; if it is less than 5, leave it. Replace all digits to the right with zeroes.
Example: Round 6,48,372 to the nearest ten-thousand. The ten-thousands digit is 4 and the next digit is 8, so round up: 6,50,000.
Estimation is useful for checking calculations. If 3,98,750 people attend an event and about 2 lakh more arrive, the total should be near 6 lakh, not 42 lakh.
5. Read a large-number statement carefully
Words such as “million,” “lakh,” “crore,” and “billion” describe different group sizes. Translate the words into digits, add commas using one consistent system, and then check the order of magnitude.
For instance, 2.5 million = 2,500,000 = 25 lakh. The decimal 2.5 means two and a half groups of one million, not 2 million plus 5.
Common errors to avoid
- Do not mix Indian and international comma grouping in one reading.
- Do not remove zeroes that hold empty places.
- Compare from the greatest place value, not from the last digit.
- When rounding, inspect the digit immediately to the right of the rounding place.
Practice: read, compare and estimate
1. Write 6,08,04,219 in words using the Indian system.
Answer: Six crore eight lakh four thousand two hundred nineteen.
2. Write 6,08,04,219 using international comma grouping.
Answer: 60,804,219.
3. Which is greater: 4,78,95,000 or 4,87,05,000?
Answer: 4,87,05,000 is greater because 87 lakh exceeds 78 lakh.
4. Round 9,76,482 to the nearest lakh.
Answer: The ten-thousands digit is 7, so round 9 lakh up to 10 lakh: 10,00,000.
5. A stadium has 48,750 seats. Estimate the number of seats in 4 such stadiums by rounding to the nearest thousand first.
Answer: 48,750 ≈ 49,000; 4 × 49,000 = about 1,96,000 seats, or about 2 lakh.
Chapter summary
Place value gives every digit a value based on its position. Indian and international systems group the same digits differently when writing commas and number names. Compare from the greatest place, round using the next digit and use estimation to check whether an answer is sensible.
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