The same digit can be worth 5 or 5 crore, depending only on where it sits. Learn how position gives value, and how lakh, crore and arab fit with million and billion.
Every digit in a number tells two stories: what it looks like on its own, and what it is worth because of where it sits. The same digit 5 can mean 5 rupees or 5 crore rupees. Understanding both stories, and how they change between the International system and the Indian and Pakistani system, is the foundation for reading any large number correctly.
The face value of a digit is simply the digit itself. It does not depend on where the digit stands in the number. The face value of 7 is always 7, whether it sits in the ones place or the millions place.
In the number 7,392, the face value of 7 is 7 and the face value of 3 is 3. Position never changes face value.
The place value of a digit is what it is worth because of its position. It equals the digit multiplied by the value of its column (ones, tens, hundreds and so on).
In 7,392, the digit 7 is in the thousands column, so its place value is 7 × 1,000 = 7,000. The digit 3 is in the hundreds column, so its place value is 3 × 100 = 300. The digit 9 is in the tens column: 9 × 10 = 90. The digit 2 is in the ones column: 2 × 1 = 2.
Check: 7,000 + 300 + 90 + 2 = 7,392. ✓
This mixes up face value (the digit alone) with place value (the digit’s worth based on position). It is the most common confusion in this topic.
The fix: the face value of 7 is 7. The place value of 7 in 7,392 is 7,000, because it sits in the thousands column. Same digit, two different questions, two different answers.
Writing a number as the sum of the place values of its digits is called expanded form. Zeros are left out, because their place value is 0.
Write 3,406,052 in expanded form.
3,406,052 = 3,000,000 + 400,000 + 6,000 + 50 + 2.
The zero in the ten-thousands column and the zero in the hundreds column have a place value of 0, so we do not write them. Check: 3,000,000 + 400,000 = 3,400,000; + 6,000 = 3,406,000; + 50 = 3,406,050; + 2 = 3,406,052. ✓
Tap any digit below to reveal its place value and face value. Then switch systems to see how the same digit's place value changes name between the International and Indian/Pakistani systems.
Tap a digit above to see its place value and face value.
The International system is used in the USA, the UK and most of the world. It groups digits in sets of three, separated by commas: ones, thousands, millions, billions.
| Place | Value | Position from the right |
|---|---|---|
| Ones | 1 | 1st |
| Tens | 10 | 2nd |
| Hundreds | 100 | 3rd |
| Thousands | 1,000 | 4th |
| Ten Thousands | 10,000 | 5th |
| Hundred Thousands | 100,000 | 6th |
| Millions | 1,000,000 | 7th |
| Ten Millions | 10,000,000 | 8th |
| Hundred Millions | 100,000,000 | 9th |
| Billions | 1,000,000,000 | 10th |
Comma rule: starting from the right, place a comma after every group of 3 digits. The number 342567891 becomes 342,567,891 (three hundred and forty-two million, five hundred and sixty-seven thousand, eight hundred and ninety-one).
India, Pakistan and nearby countries also use a second grouping system. It is built around the lakh (100,000) and the crore (10,000,000). It is common in everyday use, newspapers and money amounts in these countries.
| Place | Value | Position from the right |
|---|---|---|
| Ones | 1 | 1st |
| Tens | 10 | 2nd |
| Hundreds | 100 | 3rd |
| Thousands | 1,000 | 4th |
| Ten Thousands | 10,000 | 5th |
| Lakhs | 1,00,000 | 6th |
| Ten Lakhs | 10,00,000 | 7th |
| Crores | 1,00,00,000 | 8th |
| Ten Crores | 10,00,00,000 | 9th |
| Arabs | 1,00,00,00,000 | 10th |
Comma rule: the rightmost group has 3 digits, and every group after that has only 2 digits. The number 342567891 becomes 34,25,67,891 (thirty-four crore, twenty-five lakh, sixty-seven thousand, eight hundred and ninety-one).
The names continue upwards: 100 arab is 1 kharab (1011). The next names are used rarely, so for school work you mainly need lakh, crore and arab.
Comma placement is not interchangeable. Reading Indian place names with International commas, or the other way round, gives the wrong number.
The fix: regroup the digits using the system’s own rule. The digits 34567891 are 34,567,891 in the International system (34 million). In the Indian system the same digits are 3,45,67,891 (3 crore 45 lakh). Never mix the two.
| Indian / Pakistani Term | Value | International Equivalent |
|---|---|---|
| 1 lakh | 1,00,000 | 100 thousand |
| 10 lakh | 10,00,000 | 1 million |
| 1 crore | 1,00,00,000 | 10 million |
| 10 crore | 10,00,00,000 | 100 million |
| 1 arab | 1,00,00,00,000 | 1 billion |
| 1 kharab | 1,00,00,00,00,000 | 100 billion |
100 thousand = 1 lakh. 100 lakh = 1 crore. 100 crore = 1 arab. 100 arab = 1 kharab. Every “hundred” of one unit makes the next unit, which is a very regular pattern.
Rewrite 53,482,917 using Indian commas and say it in words.
Step 1: Write the digits without commas: 53482917.
Step 2: From the right, take 3 digits (917), then groups of 2: 82, 34, 5.
Answer: 5,34,82,917, which is 5 crore 34 lakh 82 thousand 917.
Rewrite 7,25,60,000 using International commas.
Step 1: Digits: 72560000. This is 7 crore 25 lakh 60 thousand.
Step 2: Group in threes from the right: 000, 560, 72.
Answer: 72,560,000, which is 72 million 560 thousand. Check: 7 crore = 70 million, and 25 lakh = 2.5 million, so 72.5 million plus 60 thousand = 72.56 million. ✓
A project is reported as costing “45 arab rupees”. In the Indian and Pakistani system, 45 arab is written 45,00,00,00,000. In the International system the same amount is 45,000,000,000, which is 45 billion rupees. The amount is the same. Only the grouping and names are different. Notice that the figure is not 4.5 billion: 1 arab is 1 billion, so 45 arab is 45 billion. This is exactly the kind of slip that place value helps you avoid.
A person earns Rs 85,000 a month. How much is that in a year, written with Indian commas?
Step 1: 85,000 × 12 = 1,020,000.
Step 2: Regroup: 10,20,000.
Answer: Rs 10,20,000, which is 10 lakh 20 thousand.
To compare two numbers, compare the digits from the left, one place at a time. The first place where they differ decides which number is bigger.
Compare 5,09,87,654 and 5,10,00,000.
Both have 5 crore. Next, compare the lakhs: the first number has 09 lakh and the second has 10 lakh. Since 10 is more than 09, the second number is bigger.
Check in International form: 50,987,654 and 51,000,000. ✓
Answer: 5,10,00,000 is bigger.
Round 6,48,35,912 (that is 64,835,912) to the nearest lakh and to the nearest crore.
Nearest lakh: look at the digits after the lakh place: 35,912. This is less than 50,000, so round down: 6,48,00,000.
Nearest crore: the number is 6.48 crore. Since 0.48 is less than 0.5, round down: 6,00,00,000.
Place value continues to the right of the decimal point. Each place is ten times smaller than the one before it: tenths, hundredths, thousandths.
In 4.708, the digit 4 is in the ones place (value 4). The digit 7 is in the tenths place (value 0.7). The digit 0 is in the hundredths place (value 0). The digit 8 is in the thousandths place (value 0.008).
Check: 4 + 0.7 + 0 + 0.008 = 4.708. ✓
Tap the correct answer for each question. Covers both the International and Indian/Pakistani systems.
1. The face value of 6 is 6. In 4,602,315 the 6 is in the hundred-thousands place, so its place value is 600,000.
2. Digits 24683057: groups from the right are 057, 83, 46, 2, so it is 2,46,83,057.
3. 1 crore = 100 lakh, so 2.5 crore = 2.5 × 100 = 250 lakh.
1. 3,082,945: the 8 is in the ten-thousands place, so its place value is 80,000.
2. 5,00,03,407 is 5 crore, 0 lakh, 3 thousand, 4 hundred and 7: five crore three thousand four hundred and seven. In International commas: 50,003,407.
3. 2,350,000 ÷ 100,000 = 23.5, so it is 23.5 lakh.
4. 12,50,00,000 has digits 125000000, so International form is 125,000,000. That is 125 million. In crore: 125,000,000 ÷ 10,000,000 = 12.5 crore.
A physical place-value chart, or even a chart drawn on paper with columns, helps students see why the digit 0 is needed. Ask learners to read money amounts they meet in daily life (fees, prices of a phone or a motorbike, newspaper figures) in both systems. Students who live in South Asia often hear lakh and crore at home but write International commas at school, so make the two systems explicit and practise converting. Encourage students to say the number aloud in words, which exposes mistakes such as reading 1,00,000 as “ten thousand”.
The words “lakh” and “crore” come from older Indian words (laksha and koti) and have been used in South Asia for a very long time. The grouping of commas, however, is a separate matter of printing style, and different regions use different habits.
12 questions. Select an answer for each, then submit to see your score instantly.