What is place value?
Every digit in a number has a position, and that position tells you what the digit is worth.
How the digits in 5,382 are built
Take the number 5,382:
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 5 | 3 | 8 | 2 |
| 5 × 1,000 | 3 × 100 | 8 × 10 | 2 × 1 |
The 5 isn’t just “five” — it means five thousand because it sits in the thousands place.
Going bigger: up to millions
As numbers grow, we add more places to the left:
| Millions | Hundred-thousands | Ten-thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Each place is 10 times the value of the place to its right.
Expanded form
Expanded form breaks a number into the value of each digit:
724,561 = 700,000 + 20,000 + 4,000 + 500 + 60 + 1
This helps us see exactly what each digit contributes.
Ones
Start at the right. The digit 2 is in the ones place — it's worth 2.
Tens
Move left. The digit 8 is in the tens place — it's worth 80 (8 × 10).
Hundreds
The digit 3 is in the hundreds place — it's worth 300 (3 × 100).
Thousands
The digit 5 is in the thousands place — it's worth 5,000 (5 × 1,000).
Pattern
Each place is 10 times bigger than the one to its right. That's the power of place value!
1 / 5
A digit's value depends entirely on its position. The same digit '5' can mean 5, 50, 500, or 5,000!
Comparing numbers
To compare two big numbers:
- Start from the leftmost digit
- Compare digit by digit, moving right
- The first digit that’s different tells you which number is bigger
Example: 463,285 vs 463,192
- Same in hundred-thousands (4), ten-thousands (6), thousands (3)
- Hundreds: 2 vs 1 — so 463,285 > 463,192
Practice
In the number 3,847,215, what is the value of the digit 4?
The 4 is in the ten-thousands place, so its value is 4 × 10,000 = 40,000.
Which number is the largest?
Compare from the left: all start with 89. The third digit is 3 in 893,012 — that's bigger than 2 or 1.
Write 600,000 + 50,000 + 3,000 + 200 + 10 + 7 as a single number (no commas).
Add each part: 600,000 + 50,000 + 3,000 + 200 + 10 + 7 = 653,217.
What is the value of the digit 7 in 2,704,318?
The 7 is in the hundred-thousands place: 7 × 100,000 = 700,000.
Which shows 405,060 in expanded form?
405,060 = 400,000 + 5,000 + 60. The zeros are placeholders — they hold the hundreds and ones places but add no value.
Challenge
Quick-Fire Round