Place Value, Decimals and Large Numbers: Year 5 Study Guide
Our number system works because each place is ten times bigger than the one to its right.
Year 5 students work with whole numbers well beyond 10 000. In 3 482 650, the 3 stands for 3 millions, the 4 for 4 hundred thousands and so on. Australian style leaves a space between groups of three digits (3 482 650) instead of commas, to avoid confusion with the decimal point in some countries.
They also extend the place value system to the right of the decimal point: tenths, hundredths and thousandths. 6.482 means 6 ones, 4 tenths, 8 hundredths and 2 thousandths.
Place value chart
| Millions | Hundred thousands | Ten thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 3 | 4 | 8 | 2 | 6 | 5 | 0 |
Rounding and estimating
To round to the nearest thousand, look at the hundreds digit. If it is 5 or more, round up. 46 382 rounds to 46 000 and 46 582 rounds to 47 000. Rounding helps estimate answers before calculating. To round decimals, look at the next digit: 3.476 rounds to 3.5 (one decimal place) and to 3.48 (two decimal places).
Thousands, tenths, etc.
Is it 5 or more?
Keep or add one.
With zeros, or drop decimals.
Multiplying and dividing by powers of ten
When you multiply by 10, every digit moves one place to the left. 4.35 × 10 = 43.5. When you multiply by 100 they move two places: 4.35 × 100 = 435. Dividing moves digits to the right: 52 ÷ 100 = 0.52. The decimal point does not move; the digits do.
| Number | × 10 | × 100 | ÷ 10 | ÷ 100 |
|---|---|---|---|---|
| 7.5 | 75 | 750 | 0.75 | 0.075 |
| 0.04 | 0.4 | 4 | 0.004 | 0.0004 |
| 320 | 3 200 | 32 000 | 32 | 3.2 |
Worked examples and common mistakes
Example: Order 0.6, 0.58 and 0.605: write each with three decimal places (0.600, 0.580, 0.605). The order is 0.58, 0.6, 0.605. Common mistakes: thinking 0.58 is larger than 0.6 because 58 > 6, adding a zero instead of moving digits when multiplying by 10 and losing a placeholder zero. Draw a place value chart to check.
Check your understanding: model answers
1. 2 700. 2. 640. 3. 0.7, since 0.70 is more than 0.65.
✨ Key Takeaways
- Each place is 10 times the one to its right.
- Round using the digit to the right.
- Multiplying by 10 moves digits left.
- Compare decimals by adding zeros.
💬 Questions for Discussion & Reflection
- Round 2 749 to the nearest hundred.
- Work out 6.4 × 100.
- Which is bigger: 0.7 or 0.65?