Place Value — Grade 3 Mathematics
In Grade 3, we extend place value to 4-digit numbers (up to 9,999). We explore the thousands column, write numbers in expanded and word form, and discover how multiplying or dividing by 10 shifts digits through the place value columns.
Thousands, Hundreds, Tens and Ones
10 hundreds make 1 thousand. A 4-digit number has four columns:
The number is 3,805 = 3,000 + 800 + 0 + 5
Multiplying and Dividing by 10
When you × 10, every digit moves one place to the left (a zero fills the ones place). When you ÷ 10, every digit moves one place to the right.
| Start | × 10 | ÷ 10 |
|---|---|---|
| 6 | 60 | 0.6 (Grade 4+) |
| 85 | 850 | 8.5 (Grade 4+) |
| 400 | 4,000 | 40 |
| 1,230 | 12,300 | 123 |
Worked Examples
Write 5,047 in expanded form.
- 5 in thousands → 5,000
- 0 in hundreds → 0
- 4 in tens → 40
- 7 in ones → 7
(We don't write 0 hundreds in expanded form.)
What is the value of the digit 7 in 7,362?
- 7 → thousands place
- Value = 7,000
What is 235 × 10?
- Each digit shifts one place left
- 2 → thousands, 3 → hundreds, 5 → tens, 0 fills ones
- 235 × 10 = 2,350
Practice Questions
1. Write 4,609 in expanded form.
2. What is the value of the digit 8 in 2,843?
3. Calculate 560 × 10.
4. Calculate 9,000 ÷ 10.
5. Put in order from smallest to largest: 3,521 / 3,125 / 3,512
Key Points to Remember
- A 4-digit number has Thousands | Hundreds | Tens | Ones.
- 10 hundreds = 1 thousand; 10 thousands = 1 ten-thousand.
- Zero is a placeholder — it keeps other digits in the correct column.
- Multiplying by 10: digits shift one place left; a zero appears in the ones place.
- Dividing by 10: digits shift one place right.