Every digit in a number has a job. Its place tells you its value — and once you see how it works, big numbers aren't scary at all.
In our number system, the position of a digit determines how much it's worth. The digit 5 can mean five, fifty, five hundred, or even five thousand — it all depends on where it sits.
Just like each house on a street has a different address, each position in a number has a different name and value. Moving one spot to the left makes a digit worth 10 times more.
Here's a place value chart showing the number 385,247:
| Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones | |
|---|---|---|---|---|---|---|
| 3300,000 | 880,000 | 55,000 | , | 2200 | 440 | 77 |
Each digit's value equals the digit times the value of its position. The 8 in the ten-thousands place is worth 8 × 10,000 = 80,000.
Base-ten blocks are a great way to see place value. A tiny cube is 1, a rod is 10, a flat is 100, and a big cube is 1,000.
Expanded form breaks a number apart to show the value of each digit. It's like taking the number apart and labeling every piece.
Expanded form helps you understand what a number really means. It's also super useful when you start adding and subtracting big numbers — you can work with each place separately!
Click or tap any digit in the number below to see its place and value. Hit the button to get a new number!
When you multiply by 10, every digit shifts one place to the left — it becomes worth 10 times more. When you divide by 10, every digit shifts one place to the right.
Multiply by 10 → digits move left (number gets bigger). Divide by 10 → digits move right (number gets smaller). The digits stay the same — only their position changes!
Test your place value skills with these problems. Answer each one, then check your work.
Type each place value, separated by + signs. Example: 3000 + 200 + 50 + 1
The value of a digit based on its position in a number. In 452, the 4 has a place value of 400.
Any of the symbols 0–9 used to write numbers.
A way to write a number showing the value of each digit. Example: 2,350 = 2,000 + 300 + 50.
The usual way to write a number using digits. Example: 2,350.
Our number system, where each place is 10 times the value of the place to its right.
A group of three digits separated by commas. The ones period has ones, tens, hundreds. The thousands period has thousands, ten-thousands, hundred-thousands.