Place Value
Understand ones through millions — digit values, expanded form, and regrouping.
1 Every digit has an address
In our number system, where a digit sits decides what it is worth. Moving one place left makes a digit worth ten times more.
In 2,500, the 2 is in the thousands place, so it means 2,000 — not 2.
2 Expanded form shows every part
Expanded form writes a number as the sum of each digit’s value: 345 = 300 + 40 + 5.
300 + 40 + 5 = 345. Each part is one digit’s value.
20,000 + 3,000 + 40 + 6 = 23,046.
3 Word form: write it in words
Word form spells the number out. Every place gets exactly one digit — empty places get a 0 placeholder.
“Two thousand forty” = 2,040.
“One hundred five” = 105 — the 0 holds the empty tens place. (Not 1005!)
4 Regrouping: ten for one
Ten of any place make one of the next: 10 ones = 1 ten, 10 tens = 1 hundred. This is the engine behind carrying and borrowing.
3 hundreds + 12 tens + 4 ones = 300 + 120 + 4 = 424. (12 tens regroup into 1 hundred + 2 tens.)
5 Common mistakes
Two place-value traps.
Wrong: the 2 in 2,500 means “2”. Right: name the place first: “2 thousands” = 2,000.
Wrong: 1005 has a thousands digit — it says “one thousand five”. Right: each place gets exactly one digit: 105, with 0 holding the tens place.
6 Quick checks
Try these yourself, then reveal the answer.
7 Key points and vocabulary
| Word | What it means |
|---|---|
| Digit | One of 0–9; a single numeral symbol. |
| Place | A digit’s position: ones, tens, hundreds, … |
| Value | What a digit is worth: digit × its place. |
| Expanded form | A number written as the sum of its digits’ values. |
| Standard form | The usual numeral, like 2,040. |
| Word form | The number written in words. |
Remember
- Name the place first, then the digit: “2 thousands”.
- Expanded form: add each digit’s value.
- Every place gets exactly one digit — 0 is the placeholder.
- 10 of a place = 1 of the next (regrouping).