What this chapter is about
This chapter helps you understand and work with very large numbers that appear in everyday life. Think about the population of India (more than one hundred crore people), the distance from Earth to the Moon (about 3,84,000 kilometres), or the money collected in a big cricket tournament. These numbers are so large that reading, writing and comparing them needs special care.
You will learn how to read and write numbers up to crores, how to use the Indian place value system correctly, and how to express large numbers in a shorter way. You will also see how to estimate and round off large numbers when an exact count is not needed.
After studying this chapter, you should be able to read any large number written in the Indian system, write numbers in words and figures, compare two large numbers quickly, and round off numbers to make calculations easier.
Key ideas
- The Indian place value system groups digits in sets: ones, tens, hundreds, then thousands (2 digits), then lakhs (2 digits), then crores (2 digits). Commas are placed after every two digits starting from the right, except the first group of three.
- 1 lakh = 1,00,000 (one followed by five zeros). 1 crore = 1,00,00,000 (one followed by seven zeros).
- To compare two large numbers, first count how many digits each has. The number with more digits is larger. If both have the same number of digits, compare from the leftmost digit.
- Estimation means finding a value close to the exact number. We round off to the nearest ten, hundred, thousand or lakh depending on how rough an answer we need.
- When rounding, look at the digit just after your rounding place. If it is 5 or more, round up; if it is less than 5, round down.
- Large numbers can be written in expanded form to show the value of each digit. For example, 23,45,678 = 20,00,000 + 3,00,000 + 40,000 + 5,000 + 600 + 70 + 8.
Formulas and facts to remember
- 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand.
- 100 thousands = 1 lakh (written 1,00,000).
- 100 lakhs = 1 crore (written 1,00,00,000).
- Place values from right: ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs, crores.
- Rounding rule: digit ≥ 5 at the cut-off place means round up; digit < 5 means round down.
Worked examples
Example 1: Writing a number in words
Write in words: 4,05,32,617
Step 1: Break the number at the commas. From left: 4 (crores), 05 (lakhs), 32 (thousands), 617 (hundreds-tens-ones).
Step 2: Read each group with its place name.
Answer: Four crore five lakh thirty-two thousand six hundred seventeen.
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Example 2: Comparing two large numbers
Which is greater: 58,43,200 or 6,12,45,000?
Step 1: Count digits. First number has 7 digits. Second number has 8 digits.
Step 2: More digits means a larger number.
Answer: 6,12,45,000 is greater.
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Example 3: Rounding to the nearest lakh
A city library has 3,48,672 books. Round this to the nearest lakh.
Step 1: The lakhs digit is 3. Look at the digit just after lakhs place (the ten-thousands place). It is 4.
Step 2: Since 4 < 5, we round down. Keep the lakhs digit as 3 and replace all digits to its right with zeros.
Answer: 3,00,000 (three lakh).
Common mistakes
Writing commas in the wrong places, such as 34,56,78 instead of 34,56,780 → always group two digits at a time after the first three from the right.
Confusing lakh and million → remember 1 lakh = 1,00,000 and 10 lakhs = 1 million = 10,00,000.
Rounding 2,45,000 to the nearest lakh as 3,00,000 → check the ten-thousands digit (4), which is less than 5, so round down to 2,00,000.
Forgetting zeros in the middle when writing in figures, writing "four lakh five thousand" as 4,5,000 instead of 4,05,000 → keep placeholders for empty positions.
Reading digits one by one instead of in groups → practise reading in groups separated by commas.
Quick revision
- 1 lakh = 1,00,000; 1 crore = 1,00,00,000.
- Place commas after every two digits from the right, except the first group of three.
- More digits means a larger number; same digits, compare from the left.
- Round up when the cut-off digit is 5 or more; round down when it is less than 5.
- Expanded form shows each digit multiplied by its place value.