Place Value — Grade 4 Mathematics
In Grade 4, we work with numbers up to 999,999 (six digits) and introduce decimal place value — tenths and hundredths — to the right of the decimal point. We also learn to scale numbers by multiplying or dividing by 10, 100, and 1,000.
Six-digit Place Value Chart
H. Thousands
3
T. Thousands
4
Thousands
7
Hundreds
2
Tens
0
Ones
9
The number is 347,209 = 300,000 + 40,000 + 7,000 + 200 + 9
Decimal Place Value — Tenths and Hundredths
Tens
1
Ones
6
·
.
Tenths
3
Hundredths
8
The number is 16.38 = 10 + 6 + 3/10 + 8/100
💡 Tenths means ÷10 (0.1 each), hundredths means ÷100 (0.01 each). The decimal point separates whole numbers from parts.
Scaling by 10, 100 and 1,000
| Start | × 10 | × 100 | × 1,000 |
|---|---|---|---|
| 7 | 70 | 700 | 7,000 |
| 45 | 450 | 4,500 | 45,000 |
| 0.6 | 6 | 60 | 600 |
| Start | ÷ 10 | ÷ 100 | ÷ 1,000 |
|---|---|---|---|
| 5,000 | 500 | 50 | 5 |
| 820 | 82 | 8.2 | 0.82 |
Worked Examples
Example 1 — Six-digit Expanded Form
Write 203,056 in expanded form.
- 2 in hundred-thousands → 200,000
- 0 in ten-thousands → 0
- 3 in thousands → 3,000
- 0 in hundreds → 0
- 5 in tens → 50
- 6 in ones → 6
Example 2 — Decimal Place Value
In the number 8.47, what is the value of the digit 4?
- 8 → ones (8), 4 → tenths, 7 → hundredths
- The digit 4 is in the tenths place
- Its value is 0.4 (four tenths)
Example 3 — Scaling
A factory makes 340 bolts per hour. How many does it make in 100 hours?
- 340 × 100 = digits shift two places left
- 340 × 100 = 34,000 bolts
Practice Questions
1. What is the value of the digit 5 in 156,023?
✅ The digit 5 is in the ten-thousands place. Value = 50,000.
2. Write 450,307 in expanded form.
✅ 400,000 + 50,000 + 300 + 7
3. In 9.63, what is the value of the digit 6?
✅ The digit 6 is in the tenths place. Value = 0.6
4. Calculate 47 × 1,000.
✅ Digits shift 3 places left: 47,000
5. Calculate 8,400 ÷ 100.
✅ Digits shift 2 places right: 84
Key Points to Remember
- Six-digit numbers go up to 999,999 — the columns are H.Th | T.Th | Th | H | T | O.
- The decimal point separates whole numbers (left) from parts (right).
- Tenths = 1/10 = 0.1; Hundredths = 1/100 = 0.01.
- Multiplying by 10/100/1,000 shifts all digits 1/2/3 places left.
- Dividing by 10/100/1,000 shifts all digits 1/2/3 places right.