What is Place Value?
Place value refers to the value of a digit depending on its position in a number. Each position in a number represents a power of 10.
Example: If number is 4527
| Digit | Place | Place Value |
|---|---|---|
| 4 | Thousands | 4 × 1000 = 4000 |
| 5 | Hundreds | 5 × 100 = 500 |
| 2 | Tens | 2 × 10 = 20 |
| 7 | Ones | 7 × 1 = 7 |
4527 = 4000 + 500 + 20 + 7
👉 Place value helps us read large numbers correctly.
Place Value of Digit
The place value of a digit = Digit × Value of its place
Example 1:
Find place value of 6 in 8645
6 is in hundreds place
Place value = 6 × 100 = 600
Example 2:
Place value of 9 in 9,31,542
9 is in lakh place
Place value = 9 × 1,00,000 = 9,00,000
Place Value Chart
Place value charts help students understand the position of digits clearly.
Indian Place Value Chart
| Crores | Ten Lakhs | Lakhs | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|---|
| 1,00,00,000 | 10,00,000 | 1,00,000 | 10,000 | 1000 | 100 | 10 | 1 |
Example:
If Number is 3,45,67,891 , it is read as:
Three crore forty five lakh sixty seven thousand eight hundred ninety one
International Place Value Chart
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Example:
3,456,789
Read as:
Three million four hundred fifty six thousand seven hundred eighty nine
Indian System vs International System
| Feature | Indian System | International System |
|---|---|---|
| Comma placement | 3,2,2 pattern | 3,3,3 pattern |
| Example | 12,34,56,789 | 123,456,789 |
| Terms Used | lakh, crore | million, billion |
Comparison Example
| Number | Indian System | International System |
|---|---|---|
| 100000 | 1,00,000 (1 lakh) | 100,000 (hundred thousand) |
| 1000000 | 10,00,000 (10 lakh) | 1,000,000 (1 million) |
| 10000000 | 1,00,00,000 (1 crore) | 10,000,000 (10 million) |
Place Value in Decimals
Place value in decimals tells us the value of digits to the right of the decimal point (.) Just as tens, hundreds, thousands increase by 10 times to the left, decimal places decrease by 10 times to the right.
Decimal Place Value Chart
| Thousands | Hundreds | Tens | Ones | Decimal | Tenths | Hundredths | Thousandths | Ten-Thousandths |
|---|---|---|---|---|---|---|---|---|
| 1000 | 100 | 10 | 1 | . | 1/10 | 1/100 | 1/1000 | 1/10000 |
Each step to the right divides the value by 10
Example pattern:
1 → 0.1 → 0.01 → 0.001 → 0.0001
Names of decimal places
| Place | Value | Example |
|---|---|---|
| Tenths | 1/10 | 0.5 |
| Hundredths | 1/100 | 0.25 |
| Thousandths | 1/1000 | 0.125 |
| Ten-thousandths | 1/10000 | 0.0125 |
Understanding Decimal Place Value by example
Example: 5.368
| Ones | Decimal | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 5 | . | 3 | 6 | 8 |
Place value of 3 = 0.3
Place value of 6 = 0.06
Place value of 8 = 0.008
Example: 9.482
| Digit | Place | Place Value |
|---|---|---|
| 9 | Ones | 9 |
| 4 | Tenths | 0.4 |
| 8 | Hundredths | 0.08 |
| 2 | Thousandths | 0.002 |
Expanded Form of Decimal Numbers
Expanded form helps understand the value clearly.
Example:
62.409
Expanded form:
60 + 2 + 0.4 + 0.009
Comparing Decimal Numbers using Place Value
Example:
Compare 0.45 and 0.405
Write place values:
0.45 = 45 hundredths
0.405 = 405 thousandths
0.45 > 0.405