Large numbers and place value
A small dairy may make 200 litres of milk a day. A big dairy in a city makes 1,00,000 litres a day , one lakh litres. To handle such numbers, we need to know the place value of each digit.
What is this?
In the Indian number system, we read large numbers using lakhs and crores. The places, from right to left, are:
- Ones (1)
- Tens (10)
- Hundreds (100)
- Thousands (1,000)
- Ten-thousands (10,000)
- Lakhs (1,00,000)
- Ten-lakhs (10,00,000)
- Crores (1,00,00,000)
The commas are not random. In the Indian system, the first comma sits after 3 digits from the right, then every 2 digits after that. So the number "one lakh twenty-five thousand" is written 1,25,000.
Each digit's place value is the digit times the value of its place. In 1,25,000:
- 1 is in the lakhs place → 1 × 1,00,000 = 1,00,000
- 2 is in the ten-thousands place → 2 × 10,000 = 20,000
- 5 is in the thousands place → 5 × 1,000 = 5,000
- The rest are zero.
Adding the place values gives back the number.
Reading: read the lakh first, then the thousands, then the remaining. "1 lakh, 25 thousand."
Comparing big numbers: count the digits first. The number with more digits is bigger. If they have the same number of digits, compare from the leftmost digit.
Worked examples
Example 1. Write 2,45,860 in words.
- 2 lakh, 45 thousand, 8 hundred and 60.
- "Two lakh, forty-five thousand, eight hundred sixty."
Example 2. What is the place value of 7 in 3,74,000?
- 7 is in the ten-thousands place.
- Place value = 7 × 10,000 = 70,000.
Example 3. Arrange in increasing order: 95,420; 1,02,300; 89,750; 1,12,560.
- 89,750 (5 digits) < 95,420 (5 digits) < 1,02,300 (6 digits) < 1,12,560 (6 digits).
Try it
- Write 3,67,205 in words.
- Write "five lakh, twenty thousand, three hundred" in figures.
- What is the place value of 4 in 4,52,900?
- Which is bigger: 99,999 or 1,00,000?
- Arrange: 2,45,000; 24,500; 2,04,500; 2,54,000 , in increasing order.
Hands-on
Lakh bundles. Imagine a bundle of 100 ten-rupee notes , that is ₹1,000. How many such bundles make ₹1,00,000? (100 bundles.) Picture the stack , that is what one lakh looks like.
Big number search. Find one big number in a newspaper headline (population, money, votes). Read it aloud in the Indian way. Write down each digit's place value.